脉冲时滞神经网络的全局稳定性研究
|
摘要
脉冲时滞神经网络是时滞大系统的一个重要组成部分,具有十分丰富的动力学属性.鉴于它在信号处理、动态图像处理以及全局优化等问题中的重要应用,近年来脉冲时滞神经网络的动力学问题引起了学术界的广泛关注.尤其是脉冲时滞神经网络平衡点和周期解的全局稳定性(包括渐近稳定性、指数稳定性、绝对稳定性等)得到了深入的研究,也出现了一系列深刻的结果。本文主要对三类时滞神经网络(即,Hopfield神经网络、细胞神经网络和双向联想记忆神经网络)的平衡点和周期解的全局渐近稳定性和指数稳定性进行了一系列的研究,取得了一些较深刻的结果。具体地说,本论文涉及到如下内容:
①时滞神经网络的脉冲稳定化
由于脉冲控制理论的复杂性,尤其是脉冲时滞系统稳定性分析的困难性,我们讨论了Hopfield型脉冲时滞神经网络的稳定化问题。通过设计脉冲控制器使系统全局(鲁棒)稳定。提出了明确的鲁棒脉冲控制器的设计步骤,并给出了具体模型的数值模拟。
②多时滞脉冲细胞神经网络的稳定性分析
运用参数一阶模型转换技术、Lyapunov-Krasovskii稳定性定理和LMI方法将模型线性化,得到了几个具有较少约束的新的线性矩阵不等式形式的时滞相关和时滞无关的渐近稳定性或指数稳定性标准。根据条件,可以对时滞参数的稳定域进行估计。
③脉冲对时滞细胞神经网络的指数稳定性的影响
针对当前许多脉冲时滞神经网络的稳定性结论均要求原时滞系统Lyapunov稳定的弊端,结合推广的Halanay不等式,得到了几个保证系统零解指数稳定的充分条件,克服了对脉冲强度的限制。通过对条件的分析,我们还可以对脉冲强度或脉冲间隔进行估计,对实际脉冲时滞系统的设计具有较强的指导作用。
④脉冲时滞BAM神经网络周期解的存在性和指数稳定性
运用Mawhin的重合度理论的连续性定理和Lyapunov稳定性定理,分析了具有时变时滞的脉冲双向联想神经网络的周期解的存在性和稳定性问题,得到了系统具有指数稳定的周期解的充分条件。通过与文献中相关结果的比较,可以看到我们的结果具有更好的适用性。
⑤脉冲时滞神经网络周期解的存在性和指数稳定性
运用控制压缩定理研究了脉冲神经网络的周期解的存在性和稳定性,与应用Mawhin的重合度理论的连续定理证明周期解的存在性相比,过程更简洁,需要的条件更宽松。
⑥带有leakage时滞的神经网络周期解的指数稳定性
Leakage时滞的存在给我们的研究带来了巨大的困难,这是迄今为止人们极少研究它的原因。利用模型转化技术,作者尝试着研究了带有leakage时滞的神经网络周期解的渐近和指数稳定性,得到了几个新颖的依赖leakage时滞的全局渐近和指数稳定的充分条件。
As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dynamical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums and/or periodic solutions of delayed neural networks with impulses have been derived via Lyapunov-type function/functional approaches. A series of significative results have been obtained. This thesis mainly focuses on the global stability for three types of delayed neural networks with impulse. Specifically, the main contents are as follows:
①Impulsive stabilization of delayed neural networks
Due to the complexity and imperfection of impulsive control theory for delayed systems, to the best of the author’s knowledge, stabilization of delayed systems via impulsive control approach has few results. In this thesis, the impulsive stabilization of the Hopfield-type delayed neural networks with and without uncertainty is investigated. A simple approach to the design of an impulsive controller is then presented. Two numerical examples are given for illustration of the theoretical results.
②Delay-dependent and delay-independent stability criteria for cellular neural networks with impulses and delay
Several novel delay-dependent and delay-independent asymptotical/exponential stability criteria with less restriction are established by employing parameterized first-order model transformation, Lyapunov-Krasovskii stability theorem and LMI technique in virtue of the linearization of considered model. The stability regions with respect to the delay parameters are formulated by applying the proposed results.
③Effects of delay on exponential stability of cellular neural networks with delay
We investigate the global exponential stability conditions of the delayed neural networks with impulses by means of Lyapunov-like stability theorem, generalized Halanay inequalities. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse interval can be estimated by applying the proposed results.
④Existence and exponential stability of periodic solution of BAM Neural Networks with impulse and time-varying delay
By using the continuation theorem of coincidence degree theory and Lyapunov-Krasovskii function, the existence and global exponential stability of periodic solution for BAM model of neural network with impulses and time-delay are investigated. Sets of easily verifiable sufficient conditions are obtained for the existence and global stability of periodic solution. By contrast with the recent results in the literature, our results are much more universal application.
⑤Existence and exponential stability of periodic solutions of impulsive cellular neural networks with delays
The global periodicity of cellular neural network with impulses and time-delay is studied. Several conditions guaranteeing the existence, uniqueness, and global exponential stability of periodic solution are obtained, which improve and extend some previous results. The activation functions need not be differentiable, monotone or bounded. Some numerical examples are given to illustrate the effectiveness of our results
⑥Exponential stability of periodic solution of cellular neural networks with impulses and leakage delay
Because time delays in the leakage terms are usually not easy to handle such delays have been rarely considered in the neural network community so far. By using a model transformation, a leakage delay dependent sufficient condition is derived. Systems contain many known systems as special cases and the sufficient conditions should also contain some existing results as special cases.
①时滞神经网络的脉冲稳定化
由于脉冲控制理论的复杂性,尤其是脉冲时滞系统稳定性分析的困难性,我们讨论了Hopfield型脉冲时滞神经网络的稳定化问题。通过设计脉冲控制器使系统全局(鲁棒)稳定。提出了明确的鲁棒脉冲控制器的设计步骤,并给出了具体模型的数值模拟。
②多时滞脉冲细胞神经网络的稳定性分析
运用参数一阶模型转换技术、Lyapunov-Krasovskii稳定性定理和LMI方法将模型线性化,得到了几个具有较少约束的新的线性矩阵不等式形式的时滞相关和时滞无关的渐近稳定性或指数稳定性标准。根据条件,可以对时滞参数的稳定域进行估计。
③脉冲对时滞细胞神经网络的指数稳定性的影响
针对当前许多脉冲时滞神经网络的稳定性结论均要求原时滞系统Lyapunov稳定的弊端,结合推广的Halanay不等式,得到了几个保证系统零解指数稳定的充分条件,克服了对脉冲强度的限制。通过对条件的分析,我们还可以对脉冲强度或脉冲间隔进行估计,对实际脉冲时滞系统的设计具有较强的指导作用。
④脉冲时滞BAM神经网络周期解的存在性和指数稳定性
运用Mawhin的重合度理论的连续性定理和Lyapunov稳定性定理,分析了具有时变时滞的脉冲双向联想神经网络的周期解的存在性和稳定性问题,得到了系统具有指数稳定的周期解的充分条件。通过与文献中相关结果的比较,可以看到我们的结果具有更好的适用性。
⑤脉冲时滞神经网络周期解的存在性和指数稳定性
运用控制压缩定理研究了脉冲神经网络的周期解的存在性和稳定性,与应用Mawhin的重合度理论的连续定理证明周期解的存在性相比,过程更简洁,需要的条件更宽松。
⑥带有leakage时滞的神经网络周期解的指数稳定性
Leakage时滞的存在给我们的研究带来了巨大的困难,这是迄今为止人们极少研究它的原因。利用模型转化技术,作者尝试着研究了带有leakage时滞的神经网络周期解的渐近和指数稳定性,得到了几个新颖的依赖leakage时滞的全局渐近和指数稳定的充分条件。
As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dynamical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums and/or periodic solutions of delayed neural networks with impulses have been derived via Lyapunov-type function/functional approaches. A series of significative results have been obtained. This thesis mainly focuses on the global stability for three types of delayed neural networks with impulse. Specifically, the main contents are as follows:
①Impulsive stabilization of delayed neural networks
Due to the complexity and imperfection of impulsive control theory for delayed systems, to the best of the author’s knowledge, stabilization of delayed systems via impulsive control approach has few results. In this thesis, the impulsive stabilization of the Hopfield-type delayed neural networks with and without uncertainty is investigated. A simple approach to the design of an impulsive controller is then presented. Two numerical examples are given for illustration of the theoretical results.
②Delay-dependent and delay-independent stability criteria for cellular neural networks with impulses and delay
Several novel delay-dependent and delay-independent asymptotical/exponential stability criteria with less restriction are established by employing parameterized first-order model transformation, Lyapunov-Krasovskii stability theorem and LMI technique in virtue of the linearization of considered model. The stability regions with respect to the delay parameters are formulated by applying the proposed results.
③Effects of delay on exponential stability of cellular neural networks with delay
We investigate the global exponential stability conditions of the delayed neural networks with impulses by means of Lyapunov-like stability theorem, generalized Halanay inequalities. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse interval can be estimated by applying the proposed results.
④Existence and exponential stability of periodic solution of BAM Neural Networks with impulse and time-varying delay
By using the continuation theorem of coincidence degree theory and Lyapunov-Krasovskii function, the existence and global exponential stability of periodic solution for BAM model of neural network with impulses and time-delay are investigated. Sets of easily verifiable sufficient conditions are obtained for the existence and global stability of periodic solution. By contrast with the recent results in the literature, our results are much more universal application.
⑤Existence and exponential stability of periodic solutions of impulsive cellular neural networks with delays
The global periodicity of cellular neural network with impulses and time-delay is studied. Several conditions guaranteeing the existence, uniqueness, and global exponential stability of periodic solution are obtained, which improve and extend some previous results. The activation functions need not be differentiable, monotone or bounded. Some numerical examples are given to illustrate the effectiveness of our results
⑥Exponential stability of periodic solution of cellular neural networks with impulses and leakage delay
Because time delays in the leakage terms are usually not easy to handle such delays have been rarely considered in the neural network community so far. By using a model transformation, a leakage delay dependent sufficient condition is derived. Systems contain many known systems as special cases and the sufficient conditions should also contain some existing results as special cases.
引文
[1] L.O.Chua. Passinity and complexity, IEEE Trans. Circuits Syst., 1999,46(1): 77-82.
[2] McCulloch W. Pitts W. A logical calculus of the ideas immanent in neuron activity. Bulletion Math. Biophys., 1943, 5:115-133.
[3] D.Hebb, The organization of Behavior, Wiley, New York, 1949.
[4] Minsky M. Papert S. Perceptron, MIT Press, Cambridge, MA, 1969.
[5] J.Hopfield. Neural networks and physical systems with emergent collective computational abilities, In: Proc.Natl.Acad. Sci.USA.Biophysics, 1982, 79: 2554-2558.
[6] J.Hopfield, Neurons wigh graded response have collective computational properties like those of two-state neurons. In: Proc.Natl.Acad. Sci. USA, Biophysics. 1988,81: 3088-3092.
[7] B.Kosko, Constructing an associative memory, BYTE, Sept., 1987,137-144.
[8] M. Cohen, S.Grosberg, Absolute stability of global pattern formation and parallel memory storage by compititive neural networks. IEEE Trans. on SYST.Man &Cyber., 1983, 13: 815-826.
[9] S.Grosberg, Nonlinear neural networks: principles, mechanisms, and architectures, Neural Networks, 1988,1: 17-61.
[10] L. O. Chua, L. Yang, Cellular Neural Networks: Theory. IEEE Trans. Circuits Systems, 1988, 35(10): 1257-1272.
[11] L. O. Chua, L. Yang, Cellular Neural Networks: Application. IEEE Transactions on Circuits and Systems, 1988, 35: 1273-1290.
[12] L.O. Chua, CNN: Vision of complexity, Int. J. Bifur. Chaos, 1997, 7(10): 2219-2425.
[13] L.O.Chua, T.Roska, The paradigm, IEEE Trans. Circuits Syst. I, 1993,40(3): 147-156.
[14] K.R.Crounse, L.O.Chua, Methods for image processing and pattern formation in cellular neural networks: A tutorial, IEEE Trans. Circuits Syst. I. 1995, 42(10): 583-601.
[15] R.Dogaru, L.O.Chua, Universal CNN cells, Int. J.Bifur. Chaos, 1999, 9(1): 1-48.
[16] 王明敏. 基于模板自适应细胞神经网络的图像处理及识别,上海大学学报,自然科学版.,1998,4(2): 175-179.
[17] 赵建业,余道衡. 用细胞神经网络实现图像恢复的一种新方法,电子科学学刊,1999, 21(2): 168-174.
[18] Roska T, Chua L. O. Cellular neural networks with nonlinear and delay-type template. Int. J Circuit Theory Appl., 1992, 20: 469-481.
[19] Liao Xiaofeng, Chen Guanrong,Edgar N. Sanchez.LMI-based Approach for Asymptotically Stability Analysis of Delayed Neural Networks.IEEE Transactions on CAS-I, 2002, 49 (7):1033-1039.
[20] Li Chuandong, Liao Xiaofeng.Global robust asymptotical stability of multi-delayed interval neural networks: An LMI Approach.Physics Letters A, 2004,328(3):452-462.
[21] Liao Xiaofeng, Kwok-Wo Wong, Yang Shizhong.Stability analysis for delayed cellular neural networks based on linear matrix inequality approach.Int. J. Bifurcation and Chaos, 2004, 14(9):3377-3384.
[22] Dong M.F. Global exponential stability and existence of periodic solutions of CNNs with delays. Phys. Lett. A, 2002, 300: 49–57.
[23] J.D.Cao, Global stability conditions for delayed CNNs, IEEE Trans. CAS-I 2001,48: 1330-1333.
[24] Cao J.D. Global exponential stability and periodic solutions of delayed cellular neural networks. Journal of Computer and System Sciences, 2000, 60(1): 38-46.
[25] Li X, Huang L, Wu J. Further results on the stability of delayed cellular neural networks. IEEE Transactions on Circuits and Systems I, 2003, 50(9): 1239-1242.
[26] Q. Zhang, X. Wei, J. Xu, Delay-dependent exponential stability of cellular neural networks with time-varying delays,Chaos, Solitons and Fractals, 2005, 23: 1363–1369.
[27] Liao X. F, Li C. D. An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D, 2005, 200: 139-155.
[28] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs. IEEE Trans. Circuits Syst. I ,1998, 45: 168–171.
[29] Zhang Q, Wei X, Xu J. On global exponential stability of delayed cellular neural networks with time-varying delays. Applied Mathematics and Computation, 2005, 162 (12): 679-686.
[30] Liu Y, Tang W. Exponential stability of fuzzy cellular neural networks with constant and time-varying delays. Physics Letters A 2004, 323(3-4): 224-233.
[31] Li X, Huang L. Exponential stability and global stability of cellular neural networks. Applied Mathematics and Computation 2004, 147(3): 843-853.
[32] Zhang J. Global stability analysis in delayed cellular neural networks. Computers and Mathematics with Applications 2003, 45(10-11): 1707-1720.
[33] Liao X. F, Wu Z, Yu J. Stability analyses of cellular neural networks with continuous time delay. Journal of Computational and Applied Mathematics 2002, 143(1): 29-47.
[34] Cao J.D, Li Q. On the exponential stability and periodic solutions of delayed cellular neural networks. Journal of Mathematical Analysis and Applications, 2000, 252(1): 50-64.
[35] Singh V. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks, 2004, 15(1) :223-225.
[36] Zeng Z, Wang J, Liao X. Stability analysis of delayed cellular neural networks described using cloning templates. IEEE Transactions on Circuits and Systems I, 2004, 51(11): 2313-2324.
[37] Cao J. D. A set of stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits and Systems I ,2001, 48(4): 494-498.
[38] Niculescu S. –I. Delay effects on stability: A robust approach. Springer-Verlag, Germany, 2001.
[39] Liao Xiaofeng, Chen Guanrong, Edgar N. Sanchez.Delay-dependent Exponential Stability Analysis of Delayed Neural Networks: A LMI Approach.Neural Networks, 2002, 15 (2):855-866.
[40] 周怀梧,医药生物数学,人民卫生出版社,1990.
[41] 崔克检,不等剂量的周期外给药模型,生物数学学报, 2001(2): 183-187
[42] Mil,man, V.D and Myshkis, A.D.On the stability of motion in the presence of impulses,Sib.Math J., 1960, 1: 233-237.
[43] Myshkis, A.D. and Samoilenko, A.M. Systems with impulses with prescribed moments of time. Mat.Sbornik., 1967, 74: 202-208.
[44] V. Lakshmikantham, D. D. Bainov and P.S. Simeonov. Theory of impulsive differential equations. Singapore and Teanbeck, NJ: World Scientific, 1989.
[45] A.M. Samoilenko and N.A.Peretyuk. Impulsive differential equations. World Scientific, Singapore, 1995.
[46] K.Gopalsamy and B.G.Zhang, On delay differential equations with impulses, J. Math. Anal. Appl., 1989, 139:110-122.
[47] Shen Jianhua, Wang Zhicheng. Oscillation and asymptotic behavior of solution of delay differential equations with impulse. Ann. Of Diff.Eqs., 1994, 10(1):61-69
[48] 申建华,庚建设,具有脉冲扰动的非线性时滞微分方程,应用数学,1996,9(3),272-277.
[49] Anokhin AV. On linear impulsive systems for functional differential equations. Soviet Math. Dokl, 1986, 33: 220-223.
[50] J. Yan and J. Shen. Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions. Nonlinear Analysis, 1999, 37: 245-255.
[51] Lakshmikantham V, Liu X. Stability analysis in terms of two measures. World Scientific: Singapore, 1993.
[52] T. Yang. Impulsive control theory. Berlin: Springer-Verlag, 2001.
[53] B. Zhang , Y. Liu, Global attractivity for certain impulsive delay differential equations, Nonlinear Analysis, 2003, 52 : 725-736.
[54] S. Tang, L. Chen, Global attractivity in a “food-limited” population model with impulsive effects, J. Math. Anal. Appl., 2004, 292: 211-221.
[55] X. Liu, Impulsive stabilization and control of chaotic system, Nonlinear Analysis, 2001, 47: 1081-1092
[56] C. Li, X. Liao, Complete and lag synchronization of chaotic systems via small pulses, Chaos, Solitons and Fractals, 2004, 22: 857-867.
[57] C. Li, X. Liao, X. Zhang, Impulsive synchronization of chaotic systems, Chaos, 2005, 15 , 023104.
[58] Dishiev. A. B. and Bainov D.D., Conditions for the absence,of the phenomenon ‘beating’for systems of impulse differential equations, Bull. Inst. Math. Acad. Sin, 1985, 13(2): 237-256.
[59] V. Lakshmikantham, Liu Xinzhi, Stability criteria for impulsive differential equations in terms of two measures. J. Math. Anal. Appl., 1989,137(2): 591-604
[60] Z.H. Guan, G.R. Chen On delayed impulsive Hopfield neural networks. Neural Networks, 1999, 12: 273-280.
[61] Li YK, Lu L. Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses. Physics Letters A, 2004, 333: 62-71.
[62] H. Akca, R. Alassar, V. Covachev, Z. Covacheva, E. Al-Zahrani, Continuous-time additive Hopfield-type neural networks with impulses, J Math Anal Appl. 2004, 290: 436–451.
[63] Liao Xiaofeng, Yu Juebang.Qualitative Analysis of Bi-directional Associative Memory with Time Delay.International Journal of Circuits Theory and Applications, 1998, 26(4):219-229
[64] Liao Xiaofeng, Yu Juebang.Robust Stability of Interval Hopfield Neural Network with Time Delay. IEEE Transactions on Neural Networks, 1998, 9(5):1042～1045
[65] Liao Xiaofeng, Kwok-wo Wong, Wu Zhongfu.Novel Stability Conditions for Cellular Neural Networks with Time Delay.International Journal of Bifurcation and Chaos, 2001,11(7):1853-1864
[66] Liao Xiaofeng, Kwok-wo Wong, Wu Zhongfu, Chen Guanrong.Novel Robust Stability Criteria for Interval Delayed Hopfield Neural Networks.IEEE Transactions on CAS-I, 2001, 48(11):1355-1359.
[67] Liao Xiaofeng, Wu Zhongfu, Yu Juebang.Stability Analyses of Cellular Neural Networks with Continuous Time Delay.Journal of Computational and Applied Mathematics, 2002, 143 (4):29-47.
[68] Liao Xiaofeng, Yu Juebang,Chen Guanrong.Novel Stability Criteria for Bi-directional Associative Memory Neural Networks with Time Delays.International Journal of Circuits Theory and Applications, 2002, 30(5):519-546.
[69] Liao Xiaofeng, Kwok-wo Wong,Wu Zhongfu.Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays . IEEE Transactions on Neural Networks.2003, 14 (1):222-227.
[70] Liao Xiaofeng, Kwok-wo Wong.Global Exponential Stability of Hybrid Bidirectional Associative Memory Neural Networks with Discrete Delays.Physical Review E, 2003, 67, 042901.
[71] Liao Xiaofeng, Wang Jun, Cao Jinde.Global and Robust Stability of Interval Hopfield Neural Networks with Time-varying Delays.International Journal of Neural Systems, 2003, 13 (3):171~182 .
[72] Liao Xiaofeng, Kwok-wo Wong, Yang Shizhong.Convergence dynamics of hybrid bi-directional associtative memory neural networks with distributed delays.Physics Letters A, 2003, 316 (12):55～64 .
[73] Cao Jinde, Wang Jun, Liao Xiaofeng.Novel stability criteria for delayed cellualr neural networks.International Journal of Neural Systems, 2003, 13 (5):367～375.
[74] Liao Xiaofeng, Kwok-wo Wong.Robust Stability of interval bi-directional associative memory neural networks with time delays.IEEE Transactions on SMC-B, 2004, 34 (2):1141～1154.
[75] Liao Xiaofeng, Kwok-wo Wong.Global exponential stability for a class of retarded functional differential equations with applications in neural networks . Journal of Mathematical Analysis and Applications, 2004, 293 (1):125～148.
[76] Liao Xiaofeng,Kwok-wo Wong.Li Chuanguang.Global exponential stability for a class of generalized neural networks with distributed delays.Nonlinear Analysis: Real World Applications, 2004, 5(3):527～547.
[77] Liao Xiaofeng, Kwok-wo Wong,Leung C.Hopf bifurcation and chaos in a single delayed neuron equation with nonmonotonic activation function. Chaos, Solitons & Fractals, 2001, 12(4):1535-1547.
[78] Li Chuandong, Liao Xiaofeng.Global robust stability criteria for interval delayed neural networks via an LMI approach.IEEE Transactions on CAS-II, 2006,53(9):901-905.
[79] Cao Jinde, Wang Jun.Global Asymptotic Stability of a General Class of Recurrent Neural Networks With Time-Varying Delays.IEEE Trans. CAS-I, 2003, 50(1): 34～44.
[80] Liao T.-L.,Wang F.-C..Global stability condition for cellular neural networks with time delay.Electron. Lett.,1999, 35(16):1347～1349.
[81] T.-L. Liao, F.-C. Wang, Global stability for cellular neural networks with time delay.IEEE Trans. on Neural Networks, 2000, 11(6):1481～1484.
[82] Cao Jinde.Global stability conditions for delayed CNNs, IEEE Trans. on CAS-I,2001, 48(11): 1330～1333.
[83] Arik S., Tavsanoglu V..On the global asymptotic stability of delayed cellular neural networks.IEEE Trans. on CAS-I, 2000, 47 (4):571～574.
[84] Arik S. . An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks.IEEE Trans. on Neural Networks, 2002, 13(5):1239～1242.
[85] Arik S.An Improved Global Stability Result for Delayed Cellular Neural Networks.IEEE Trans. on CAS-I, 2002, 49 (8): 1211～1214.
[86] Hale J. K., Lunel S. M. V. . Introduction to the theory of functional differential Equations.Applied mathematical sciences, Vol. 99, New York: Springer, 1999.
[87] Liao X, Mu W, Yu J. Stability analysis of bi-directional association memory with axonal signal transmission delay. Proceedings of the third International Conference on Signal Processing, 1996, 2: 1457-1460.
[88] Liao X, Liu G, YU J. Qualitative analysis of BAM networks. Journal of circuits and systems 1996, 1: 13-18.
[89] Michel, A. N., Farrell, J. A., & Porod, W. Qualitative analysis of neural networks. IEEE Transactions on Circuits Systems I 1989, 36: 229–243.
[90] Gopalsamy K, He X. Delay-dependent stability in bi-directional associative memory networks. IEEE transaction on neural networks 1994; 5:998-1002.
[91] Arik S. Stability analysis of delayed neural networks. IEEE Transaction on circuits and systems 2000, 47(7): 1089-1092.
[92] Cao Jinde. Periodic oscillation and exponential stability of delayed CNN. Physics Letters A 2000, 270: 157–163.
[93] Gopalsamy K., & He XZ. Stability in asymmetric Hopfield networks with transmission delays. Physica D, 1994, 76: 344–358.
[94] Li Chuandong, Liao Xiaofeng, Chen Yong. On the robust stability of bidirectional associative memory neural networks with constant delays. LECTURE NOTES IN COMPUTER SCIENCE 3173: 102-107, 2004.
[95] Joy M. On the global convergence of a class of functional differential equations with application in neural network theory. Journal of Mathematical Analysis and Applications 1999, 232: 61–81.
[96] Joy M. Results concerning the absolute stability of delayed neural networks. Neural Networks 2000, 13: 613–616.
[97] Zhang Y. Global exponential stability and periodic results of delay Hopfield neural networks. International Journal of System Sciences 1996, 27:227-231.
[98] Sanchez E. N., & Perez J. P. Input-to-state stability analysis for dynamic NN. IEEE Transactions on Circuits Systems 1999, 46:1395–1398.
[99] Zhang J. Y. and Yang Y. R., Global stability analysis of bi-directional associative memory neural networks with time delay, Int. J. Circuit Theory and application, 2001, 29(2): 185-196.
[100] Hari Rao V. Sree and Bh, R. M. Phaneendra, Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones, Neural Networks, 1999, 12(3): 455-165.
[101] Li Chuandong, Liao Xiaofeng, Zhang Rong. Delay-dependent exponential stability Analysis of BAM NNs: an LMI approach. Chaos, Solitons & Fractals, 2005, 24(4) 1119-1134.
[102] Arik S. Global robust stability of delayed neural networks. IEEE Trans. CAS-I, 2003, 50 (1): 156-160.
[103] Li Daigao. Matrix theory and its applications. China: Chongqing University Press, 1988.
[104] Arik S. Global asymptotic stability of a larger class of neural networks with constant time delay. Physics Letters A, 2003, 311: 504-511.
[105] Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Physics Letters A, 2002, 297:182-190.
[106] Zhang Q. Global asymptotic stability of Hopfield neural networks with transmission delays. Physics Letters A, 2003, 318: 182-190.
[107] Roska, T., Wu, C. W., Balsi, M. and Chua, L. O. Stability and dynamics of delay-type general neural networks. IEEE Trans. Circuits Syst., 1992, 39(5): 487-490.
[108] L.O. Chua, T. Roska. Stability of a class of nonreciprocal cellular neural networks. IEEE Trans. CAS, 1990, 37(12): 1520-1527.
[109] T. Roska, C.W. Wu, M. Balsi, L.O. Chua. Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans. CAS-I, 1992, 39(6): 487-490.
[110] T. Roska, C.W. Wu, L.O. Chua. Stability of cellular neural networks with dominant nonlinear and delay-type templates, 1993, 40(4): 270-272.
[111] P. P. Civalleri, M. Gilli, L. Pandolfi. On stability of cellular neural networks with delay. IEEE Trans. CAS-I, 1993, 40 (3): 157-165.
[112] M. Gilli. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Trans. CAS-I, 1994, 41(8): 518-528.
[113] Hui Ye, N. Micheal, K. Wang. Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Trans. CAS-I, 1996, 43(7): 532-543.
[114] Y.J. Cao, Q.H. Wu. A note on stability of analog neural networks with time delays. IEEE Trans. Neural networks, 1996, 7(6): 1533-1535.
[115] N. Takashashi. L.O. Chua. On the complete stability of nonsymmetric cellular neural networks. IEEE Trans. CAS-I, 1998, 45(7): 754-758.
[116] Zhi-Hong Guan, G. Chen, Yi Qin. On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans. Neural networks, 2000, 11(2): 534-540,.
[117] Arik S. Global asymptotic stability of a class of dynamical neural networks. IEEE Trans. CAS-I, 2000, 47(4): 568-571.
[118] P. Campolucci, F. Piazza. Intrinsic stability-control method for recursive filters and neural networks. IEEE Trans. CAS-II, 2000, 47(8): 797-802.
[119] J.A.K. Suykens, B. de Moor, J. Vandewalle. Robust local stability of multilayer recurrent neural networks. IEEE Trans. Neural networks, 2000, 11(1): 222-229.
[120] Youshen Xia, Jun Wang. Global exponential stability of recurrent neural networks for solving optimization and related problems. IEEE Trans. Neural networks, 2000, 11(4): 1017-1022.
[121] Xue-Bin Liang, J. Wang. Absolute exponential stability of neural networks with a general class of activation functions. IEEE Trans. CAS-I, 2000, 47(8): 1258-1263.
[122] Xue-Bin Liang. Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons. IEEE Trans. Neural networks, 2000, 11(5): 1194-1196.
[123] X.-B. Liang, Jun Wang. A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case. IEEE Trans. CAS-I, 2000, 47(4): 609-611.
[124] N. Takahashi. A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Trans. CAS-I, 2000, 47(6): 793-799.
[125] Hong Qiao, Jigen Peng, Zong-Ben Xu. Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks. IEEE Trans. Neural networks, 2001, 12(2): 360-370.
[126] Xue-Bin Liang; J. Si. Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. IEEE Trans. Neural networks, 2001, 12(2): 349-359.
[127] Jinde Cao. A set of stability criteria for delayed cellular neural networks. IEEE Trans. CAS-I, 2001, 48(4): 494-498.
[128] Donq Liang Lee. Relaxation of the stability condition of the complex-valued neural networks. IEEE Trans. Neural networks, 2001, 12(5): 1260-1262.
[129] Wen Yu, Xiaoou Li. Some stability properties of dynamic neural networks. IEEE Trans. CAS-I, 2001, 48(2): 256-259.
[130] Xue-Bin Liang, Jun Wang. An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks. IEEE Trans. CAS-I, 2001, 48(11): 1308-1317.
[131] M. Forti. Some extensions of a new method to analyze complete stability of neural networks. IEEE Trans. Neural networks, 2002, 13(5): 1230-1238.
[132] Anping Chen, Jinde Cao, Lihong Huang. An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE Trans. CAS-I, 2002, 49(7): 1028-1032.
[133] Sanqing Hu, Jun Wang. Global stability of a class of continuous-time recurrent neural networks. IEEE Trans. CAS-I, 2002, 49(9): 1334-1347.
[134] Sanqing Hu, Jun Wang. Global stability of a class of discrete-time recurrent neural networks. IEEE Trans. CAS-I, 2002, 49(8): 1104-1117.
[135] Weirui Zhao, Wei Lin, Rongsong Liu, Jiong Ruan. Asymptotical stability in discrete-time neural networks. IEEE Trans. CAS-I, 2002, 49(10): 1516-1520.
[136] Sanqing Hu, Jun Wang. Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks. IEEE Trans. Automatic Control, 2002, 47(5): 802-807.
[137] S. Arik. A note on the global stability of dynamical neural networks. IEEE Trans. CAS-I, 2002, 49(4): 502-504.
[138] Yi Zhang, Pheng Ann Heng, P. Vadakkepat. Absolute periodicity and absolute stability of delayed neural networks. IEEE Trans. CAS-I, 2002, 49(2): 256-261.
[139] Yunong Zhang, Jun Wang. Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment. IEEE Trans. Neural networks, 2002, 13(3): 633-644.
[140] Gwo-Jeng Yu, Chien-Yu Lu, J.S.-H. Tsai, Te-Jen Su, Bin-Da Liu. Stability of cellular neural networks with time-varying delay. IEEE Trans. CAS-I, 2003, 50 (5): 677-678.
[141] Dingguo Chen, R.R. Mohler. Neural-network-based load modeling and its use in voltage stability analysis. IEEE Transactions on Control Systems Technology, 2003, 11(4): 460-470.
[142] A. Meyer-Baese, S.S. Pilyugin, Y. Chen. Global exponential stability of competitive neural networks with different time scales. IEEE Trans. Neural networks, 2003, 14(3): 716-719.
[143] Xuemei Li, Lihong Huang, Jianhong Wu. Further results on the stability of delayed cellular neural networks. IEEE Trans. CAS-I, 2003, 50(9): 1239-1242.
[144] Hong Qiao; Jigen Peng; Xu, Z.-B.; Bo Zhang. A reference model approach to stability analysis of neural networks. IEEE Transactions on Systems, Man and Cybernetics, Part B, 2003, 33 (6): 925-936.
[145] Zhigang Liu, Anping Chen, Jinde Cao, Lihong Huang. Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays. IEEE Trans. CAS-I, 2003, 50 (9): 1162-1173.
[146] Zhigang Zeng, Jun Wang, Xiaoxin Liao. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. CAS-I, 2003, 50(10): 1353-1358.
[147] Qiang Zhang, Runnian Ma, Chao Wang, Jin Xu. On the global stability of delayed neural networks. IEEE Transactions on Automatic Control, 2003, 48(5): 794-797.
[148] Xiao-xin Liao, Jun Wang. Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans. CAS-I, 2003, 50(2): 268-274.
[149] Jiing-Dong Hwang, Feng-Hsiag Hsiao. Stability analysis of neural-network inter-connected systems. IEEE Trans. Neural networks, 2003, 14(1): 201-208.
[150] Sanqing Hu, Jun Wang. Absolute exponential stability of a class of continuous-time recurrent neural networks. IEEE Trans. Neural networks, 2003, 14(1): 35-45.
[151] Jiye Zhang. Globally exponential stability of neural networks with variable delays. IEEE Trans. CAS-I, 2003, 50 (2): 288-290.
[152] V. Singh. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural networks, 2004, 15(1): 223-225.
[153] Haijun Jiang, Zhidong Teng. Boundedness and stability for nonautonomous bidirectional associative neural networks with delay. IEEE Trans. CAS-II, 2004, 51(4): 174-180.
[154] Tianping Chen, Libin Rong. Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural networks, 2004, 15(1): 203-206.
[155] Houduo Qi, Liqun Qi. Deriving sufficient conditions for global asymptotic stability of delayed neural networks via non-smooth analysis. IEEE Trans. Neural networks, 2004, 15(1): 99-101.
[156] Z. Zeng J. Wang, X. Liao. Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. CAS-I, 2004, 50(11): 2313-2324
[157] Junjie Wei, Shigui Ruan. Stability and bifurcation in a neural network model with two delays. Physica D, 1999, 130(3-4): 255-272.
[158] Hongtao Lu. On stability of nonlinear continuous-time neural networks with delays. Neural Networks, 1999, 13(10): 1135-1143.
[159] S. Blythe, Xuerong Mao, Xiaoxin Liao. Stability of stochastic delay neural networks. Journal of The Franklin Institute, 2001, 328(4): 481-495.
[160] Yuming Chen. A remark on ‘On stability of nonlinear continuous-time neural networks with delays. Neural Networks, 2001, 14(10): 1463-1469.
[161] Jigen Peng, Hong Qiao, Zong-ben Xu. A new approach to stability of neural networks with time-varying delays. Neural Networks, 2002, 15(1): 95-103.
[162] Hongyong Zhao. Global stability of bidirectional associative memory neural networks with distributed delays. Physics Letters A, 2002, 297(3-4): 182-190.
[163] He Huang, Jinde Cao, Jun Wang. Global exponential stability and periodic solutions of recurrent neural networks with delays. Physics Letters A, 2002, 298(5-6): 393-404.
[164] Yuming Chen. Global stability of neural networks with distributed delays. Neural Networks, 2002, 15(7): 867-871.
[165] Dongming Zhou, Jinde Cao. Globally exponential stability conditions for cellular neural networks with time-varying delays. Applied Mathematics and Computation, 2002, 131(2-3): 487-496.
[166] Haijun Jiang, Zhiming Li, Zhidong Teng. Boundedness and stability for nonautonomous cellular neural networks with delay. Physics Letters A, 2003, 306(5-6): 313-325.
[167] S. Mohamad, K. Gopalsamy. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation, 2003, 135(15): 17-38.
[168] Bingji Xu, Xinzhi Liu, Xiaoxin Liao. Global asymptotic stability of high-order Hopfield type neural networks with time delays. Computers and Mathematics with Applications, 2003, 45(10-11): 1729-1737.
[169] Xue-Mei Li, Li-Hong Huang, Huiyan Zhu. Global stability of cellular neural networks with constant and variable delays. Nonlinear Analysis, 2003, 53(3-4): 319-333.
[170] Anping Chen, Lihong Huang, Jinde Cao. Existence and stability of almost periodic solution for BAM neural networks with delays. Applied Mathematics and Computation, 2003, 137((1): 177-193.
[171] Boyd S., Ghaoui L.E., Feron E., Balakrishnan V..Linear Matrix Inequalities in system and Control Theory.In:Proceedings of SIAM, Philadephia, 1994.
[172] Kosko, B., Competitive. adaptative bidirectional associative. Memories. Proceedings of the IEEE. First International Conference on Neural Networks, eds M. Cardill and. C. Butter 1988, 2: 759-766
[173] Nesterov, Y., & Nemirovsky, A. Interior point polynomial methods in convex Programming. SIAM: Philadephia PA 1994.
[174] D.Bainov and V. Covachev. Impulsive differential equations with a small parameter. World Scientific, Singapore, 1994.
[175] D. D. Bainov and P.S. Simeonov. Systems with impulse effect: Stability, theory, and applications. Ellis Horwood Limited, Chichester, 1989.
[176] D. D. Bainov and P.S. Simeonov. Impulsive differential equations: Periodic solutions and applications. Longman Group UK Limited, 1993.
[177] A.F.Filippov. Differential equations with discontinuous righthand sides. Mathematics and its applications (Kluwer Academic Publisher). Soviet series. Kluwer Academic, Boston, USA, 1998.
[178] S.G.Pandit and S.G.Deo. Differential systems involving impulses. Springer-Verlag, New York, USA, 1982.
[179] Li ZG, Wen CY, Soh YC. Analysis and design of impulsive control systems. IEEE Trans Automat Contr, 2001, 46 (6): 894-903??.
[180] Lu HT. Chaotic attractors in delayed neural networks. Physics Letters A 2002; 298: 109-116.
[181] S. Arik, V. Tavsanoglu, Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing, 2000, 68: 161-176
[182] J. Cao, Global asymptotics stability of delayed bi-directional associative memory neural networks Appl. Math. Comput. 2003, 142 : 333-339.
[183] Y.H. Xia, J.D. Cao, S.S. Cheng, Global exponential stability of delayed cellular neural networks with impulses, Neurocomputing 2007, 70: 2495-2501..
[184] Z.J. Gui, W.G. Ge, Periodic solutions of nonautonomous cellular neural networks with impulses, Chaos, Solitons and Fractals, 2007, 32: 1760–1771.
[185] Y.X. Wang , W.M. Xiong , Q.Y. Zhou, B. Xiao, Y,H. Yu, Global exponential stability of cellular neural networks with continuously distributed delays and impulses, Physics Letters A, 2006, 350: 89–95.
[186] Z.J. Gui, W.G. Ge, Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses. Physics Letters A, 2006, 354: 84–94.
[187] Y.K. Li, Global exponential stability of BAM neural networks with delays and impulses, Chaos, Solitons and Fractals, 2005, 24(1): 279–285.
[188] Y.K. Li, W.Y. Xing, L.H. Lu Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solution and Fractals, 2006, 27: 437–445.
[189] A. Halanay. Differential equations: Stability, oscillations, time lags. Academic, New York, 1966.
[190] J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A, 2003, 307(2-3): 136-147.
[191] Y.K. Li, L.H. Lu Global exponential stability and existence of periodic solution of Hopfield-type neutral networks with impulses. Phys Lett A, 2004, 333: 51–61.
[192] Z.H. Guan, James L, G. Chen, On impulsive auto-associative neural networks, Neural Networks, 2000, 13: 63–69.
[193] S. Mohamad, K. Gopalsamy, Exponential stability of continuous-time and discrete-time cellular neural networks with delays, Appl.Math. Comput. 2003, 135: 17–38.
[194] A. Chen, J. Cao, L. Huang, Exponential stability of BAM neural networks with transmission delays. Neurocomputing, 2004, 57: 435-454.
[195] Kosko B., Bi-directional associative memory. IEEE transaction on Systems, Man, and Cybernetics 1998, SMC-18: 49-60.
[196] Kosko B., Adaptive Bi-directional associative memories Applied Optics 1989, 26: 4947-4960.
[197] Kosko B., Unsupervised learning in noise. IEEE transaction on neural networks, 1990, NN-1: 44-57.
[198] Kosko B., Structural stability of unsupervised learning in feedback neural networks. IEEE transaction on automatic Control 1991, AC-36: 785-790.
[199] Kosko B., Neural Networks and Fuzzy Systems-A Dynamical System Approach to Machine Intelligence, Prentice-Hall: Englewood Cliffs, NJ, 1992.
[200] Mathai C., Upadhyaya B. C., Performance analysis and application of the Bi-directional associative memory to industrial spectral signatures. Proceeding of IJCNN, ,1989, vol.1: 33-37.
[201] Elsen I., Kraiaiss K.F. and Krumbiegel D., Pixel based 3D object recognition with Bi-directional associative memory. International Conference on neural networks, 1997, 3: 1679-1684.
[202] Maundy B., EI-Masry. A switched capacitor Bi-directional associative memory. IEEE transaction on Circuits and systems 1990, 37(12):1568-1572.
[203] Hasan SMR,Siong NK. A VLSI BAM neural network chip for pattern recognition application. Proceedings of IEEE international Conference on neural networks,1995, vol. 1: 164-168.
[204] K. Gopalsmy, X.Z. He, Delay-independent stability in bidirectional associative memory networks IEEE Trans. Neural Networks, 1994, 5 : 998-1002.
[205] J. Cao, M. Dong, Exponential stability of delayed bi-directional associative memory networks Appl. Math. Comput. 2003, 135: 105-112
[206] J. Cao, L. Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays IEEE Trans. Neural Networks, 2002, 13: 457-463.
[207] S. Haykin, Neural Networks, Prentice Hall, New Jersey, 1999.
[208] S. J. Guo, L.H. Huang, B.X. Dai, Z.Z. Zhang, Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys. Lett. A, 2003, 317: 97-106.
[209] Z. Liu, A. Chen, J. Cao, L. Huang, Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays Phys. Lett. A, 2003, 319: 305-316.
[210] Y.K. Li, P. Liu, Existence and Stability of Positive Periodic Solution for BAM Neural Networks with Delays, Mathematical and Computer Modelling, 2004, 40: 757-770.
[211] T.J.Zhou, A.Chen, ,Y.Y. Zhou, Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays. Physics Letters A, 2005, 343: 336–350.
[212] Q.K. Song, J. Cao, Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction–diffusion terms. Chaos, Solitons and Fractals, 2005, 23: 421–430.
[213] M. Han, P.Bi,, Existence and bifurcation of periodic solutions of high-dimensional delay differential equations. Chaos, Solitons and Fractals, 2004, 20: 1027-1036.
[214] Z. Jin, Z.Ma, M.Han, The existence of periodic solutions of the n-species Lotka–Volterra competition systems with impulsive Chaos, Solitons and Fractals, 2004, 22: 181-188.
[215] Y. K.Li, Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays Chaos, Solitons and Fractals, 2004, 20: 459-466.
[216] X. Liu, G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations, Comput. Math.Appl., 2001, 41: 903–915.
[217] R.E. Gains, Mawhin JL.Coincidence degree and nonlinear differential equation. Berlin: Springer-Verlag, 1977.
[218] J. Dieudonn Foundations of Modern Analysis. Academic Press, New York, MR 1960 ,22:11074.
[219] S. Long and D. Y. Xu. Delay-dependent stability analysis for impulsive neural networks with time varying delays. Neurocomputing (2007), doi: 10.1016/j. neucom. 2007. 03.010. (In press)
[220] Kosko B. A dynamical systems approach to machine intelligence. Neural Networks and Fuzzy Systems, Prentice Hall, New Delhi: Prentice-Hall of India, 1992.
[221] K. Gopalsamy Leakage delays in BAM. J. Math. Anal. Appl., 2007, 325: 1117–1132.
[222] Cao J.D. On exponential stability and periodic solutions of CNNs with delays. Phys. Lett. A, 2000, 267: 312-318.
[223] Chen A.P. & Cao J.D. Almost periodic solution of shunting inhibitory CNNs with delays. Phys. Lett. A, 2000, 298: 161-170.
[224] Huang H. & Cao J.D. Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay. Phys. Lett. A, 2003, 314: 222-231.
[225] Huang H. & Cao J.D. On global asymptotic stability of recurrent neural networks with time-varying delays. Appl. Math. Comput., 2003, 142: 143-154.
[226] Jinling Liang, Jinde Cao. Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays. Physics Letters A, 2003, 314(5-6): 434-442.
[227] Qiang Zhang, Xiaopeng Wei, Jin Xu. Global exponential stability of Hopfield neural networks with continuously distributed delays. Physics Letters A, 2003, 315(6): 431-436.
[228] C. Li, X. Liao, and T. Huang. Exponential stabilization of chaotic systems with delay by periodically intermittent control. CHAOS, 2007,17, 013103, .
[229] S. Mohamad, K. Gopalsamy Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math Comput Simul., 2000, 53: 1–39.
[230] S. Mohamad, K. Gopalsamy Neuronal dynamics in time varying environments: continuous and discrete time models. Discrete Cont Dyn Syst., 2000, 6: 841–860.
[2] McCulloch W. Pitts W. A logical calculus of the ideas immanent in neuron activity. Bulletion Math. Biophys., 1943, 5:115-133.
[3] D.Hebb, The organization of Behavior, Wiley, New York, 1949.
[4] Minsky M. Papert S. Perceptron, MIT Press, Cambridge, MA, 1969.
[5] J.Hopfield. Neural networks and physical systems with emergent collective computational abilities, In: Proc.Natl.Acad. Sci.USA.Biophysics, 1982, 79: 2554-2558.
[6] J.Hopfield, Neurons wigh graded response have collective computational properties like those of two-state neurons. In: Proc.Natl.Acad. Sci. USA, Biophysics. 1988,81: 3088-3092.
[7] B.Kosko, Constructing an associative memory, BYTE, Sept., 1987,137-144.
[8] M. Cohen, S.Grosberg, Absolute stability of global pattern formation and parallel memory storage by compititive neural networks. IEEE Trans. on SYST.Man &Cyber., 1983, 13: 815-826.
[9] S.Grosberg, Nonlinear neural networks: principles, mechanisms, and architectures, Neural Networks, 1988,1: 17-61.
[10] L. O. Chua, L. Yang, Cellular Neural Networks: Theory. IEEE Trans. Circuits Systems, 1988, 35(10): 1257-1272.
[11] L. O. Chua, L. Yang, Cellular Neural Networks: Application. IEEE Transactions on Circuits and Systems, 1988, 35: 1273-1290.
[12] L.O. Chua, CNN: Vision of complexity, Int. J. Bifur. Chaos, 1997, 7(10): 2219-2425.
[13] L.O.Chua, T.Roska, The paradigm, IEEE Trans. Circuits Syst. I, 1993,40(3): 147-156.
[14] K.R.Crounse, L.O.Chua, Methods for image processing and pattern formation in cellular neural networks: A tutorial, IEEE Trans. Circuits Syst. I. 1995, 42(10): 583-601.
[15] R.Dogaru, L.O.Chua, Universal CNN cells, Int. J.Bifur. Chaos, 1999, 9(1): 1-48.
[16] 王明敏. 基于模板自适应细胞神经网络的图像处理及识别,上海大学学报,自然科学版.,1998,4(2): 175-179.
[17] 赵建业,余道衡. 用细胞神经网络实现图像恢复的一种新方法,电子科学学刊,1999, 21(2): 168-174.
[18] Roska T, Chua L. O. Cellular neural networks with nonlinear and delay-type template. Int. J Circuit Theory Appl., 1992, 20: 469-481.
[19] Liao Xiaofeng, Chen Guanrong,Edgar N. Sanchez.LMI-based Approach for Asymptotically Stability Analysis of Delayed Neural Networks.IEEE Transactions on CAS-I, 2002, 49 (7):1033-1039.
[20] Li Chuandong, Liao Xiaofeng.Global robust asymptotical stability of multi-delayed interval neural networks: An LMI Approach.Physics Letters A, 2004,328(3):452-462.
[21] Liao Xiaofeng, Kwok-Wo Wong, Yang Shizhong.Stability analysis for delayed cellular neural networks based on linear matrix inequality approach.Int. J. Bifurcation and Chaos, 2004, 14(9):3377-3384.
[22] Dong M.F. Global exponential stability and existence of periodic solutions of CNNs with delays. Phys. Lett. A, 2002, 300: 49–57.
[23] J.D.Cao, Global stability conditions for delayed CNNs, IEEE Trans. CAS-I 2001,48: 1330-1333.
[24] Cao J.D. Global exponential stability and periodic solutions of delayed cellular neural networks. Journal of Computer and System Sciences, 2000, 60(1): 38-46.
[25] Li X, Huang L, Wu J. Further results on the stability of delayed cellular neural networks. IEEE Transactions on Circuits and Systems I, 2003, 50(9): 1239-1242.
[26] Q. Zhang, X. Wei, J. Xu, Delay-dependent exponential stability of cellular neural networks with time-varying delays,Chaos, Solitons and Fractals, 2005, 23: 1363–1369.
[27] Liao X. F, Li C. D. An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D, 2005, 200: 139-155.
[28] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs. IEEE Trans. Circuits Syst. I ,1998, 45: 168–171.
[29] Zhang Q, Wei X, Xu J. On global exponential stability of delayed cellular neural networks with time-varying delays. Applied Mathematics and Computation, 2005, 162 (12): 679-686.
[30] Liu Y, Tang W. Exponential stability of fuzzy cellular neural networks with constant and time-varying delays. Physics Letters A 2004, 323(3-4): 224-233.
[31] Li X, Huang L. Exponential stability and global stability of cellular neural networks. Applied Mathematics and Computation 2004, 147(3): 843-853.
[32] Zhang J. Global stability analysis in delayed cellular neural networks. Computers and Mathematics with Applications 2003, 45(10-11): 1707-1720.
[33] Liao X. F, Wu Z, Yu J. Stability analyses of cellular neural networks with continuous time delay. Journal of Computational and Applied Mathematics 2002, 143(1): 29-47.
[34] Cao J.D, Li Q. On the exponential stability and periodic solutions of delayed cellular neural networks. Journal of Mathematical Analysis and Applications, 2000, 252(1): 50-64.
[35] Singh V. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks, 2004, 15(1) :223-225.
[36] Zeng Z, Wang J, Liao X. Stability analysis of delayed cellular neural networks described using cloning templates. IEEE Transactions on Circuits and Systems I, 2004, 51(11): 2313-2324.
[37] Cao J. D. A set of stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits and Systems I ,2001, 48(4): 494-498.
[38] Niculescu S. –I. Delay effects on stability: A robust approach. Springer-Verlag, Germany, 2001.
[39] Liao Xiaofeng, Chen Guanrong, Edgar N. Sanchez.Delay-dependent Exponential Stability Analysis of Delayed Neural Networks: A LMI Approach.Neural Networks, 2002, 15 (2):855-866.
[40] 周怀梧,医药生物数学,人民卫生出版社,1990.
[41] 崔克检,不等剂量的周期外给药模型,生物数学学报, 2001(2): 183-187
[42] Mil,man, V.D and Myshkis, A.D.On the stability of motion in the presence of impulses,Sib.Math J., 1960, 1: 233-237.
[43] Myshkis, A.D. and Samoilenko, A.M. Systems with impulses with prescribed moments of time. Mat.Sbornik., 1967, 74: 202-208.
[44] V. Lakshmikantham, D. D. Bainov and P.S. Simeonov. Theory of impulsive differential equations. Singapore and Teanbeck, NJ: World Scientific, 1989.
[45] A.M. Samoilenko and N.A.Peretyuk. Impulsive differential equations. World Scientific, Singapore, 1995.
[46] K.Gopalsamy and B.G.Zhang, On delay differential equations with impulses, J. Math. Anal. Appl., 1989, 139:110-122.
[47] Shen Jianhua, Wang Zhicheng. Oscillation and asymptotic behavior of solution of delay differential equations with impulse. Ann. Of Diff.Eqs., 1994, 10(1):61-69
[48] 申建华,庚建设,具有脉冲扰动的非线性时滞微分方程,应用数学,1996,9(3),272-277.
[49] Anokhin AV. On linear impulsive systems for functional differential equations. Soviet Math. Dokl, 1986, 33: 220-223.
[50] J. Yan and J. Shen. Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions. Nonlinear Analysis, 1999, 37: 245-255.
[51] Lakshmikantham V, Liu X. Stability analysis in terms of two measures. World Scientific: Singapore, 1993.
[52] T. Yang. Impulsive control theory. Berlin: Springer-Verlag, 2001.
[53] B. Zhang , Y. Liu, Global attractivity for certain impulsive delay differential equations, Nonlinear Analysis, 2003, 52 : 725-736.
[54] S. Tang, L. Chen, Global attractivity in a “food-limited” population model with impulsive effects, J. Math. Anal. Appl., 2004, 292: 211-221.
[55] X. Liu, Impulsive stabilization and control of chaotic system, Nonlinear Analysis, 2001, 47: 1081-1092
[56] C. Li, X. Liao, Complete and lag synchronization of chaotic systems via small pulses, Chaos, Solitons and Fractals, 2004, 22: 857-867.
[57] C. Li, X. Liao, X. Zhang, Impulsive synchronization of chaotic systems, Chaos, 2005, 15 , 023104.
[58] Dishiev. A. B. and Bainov D.D., Conditions for the absence,of the phenomenon ‘beating’for systems of impulse differential equations, Bull. Inst. Math. Acad. Sin, 1985, 13(2): 237-256.
[59] V. Lakshmikantham, Liu Xinzhi, Stability criteria for impulsive differential equations in terms of two measures. J. Math. Anal. Appl., 1989,137(2): 591-604
[60] Z.H. Guan, G.R. Chen On delayed impulsive Hopfield neural networks. Neural Networks, 1999, 12: 273-280.
[61] Li YK, Lu L. Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses. Physics Letters A, 2004, 333: 62-71.
[62] H. Akca, R. Alassar, V. Covachev, Z. Covacheva, E. Al-Zahrani, Continuous-time additive Hopfield-type neural networks with impulses, J Math Anal Appl. 2004, 290: 436–451.
[63] Liao Xiaofeng, Yu Juebang.Qualitative Analysis of Bi-directional Associative Memory with Time Delay.International Journal of Circuits Theory and Applications, 1998, 26(4):219-229
[64] Liao Xiaofeng, Yu Juebang.Robust Stability of Interval Hopfield Neural Network with Time Delay. IEEE Transactions on Neural Networks, 1998, 9(5):1042～1045
[65] Liao Xiaofeng, Kwok-wo Wong, Wu Zhongfu.Novel Stability Conditions for Cellular Neural Networks with Time Delay.International Journal of Bifurcation and Chaos, 2001,11(7):1853-1864
[66] Liao Xiaofeng, Kwok-wo Wong, Wu Zhongfu, Chen Guanrong.Novel Robust Stability Criteria for Interval Delayed Hopfield Neural Networks.IEEE Transactions on CAS-I, 2001, 48(11):1355-1359.
[67] Liao Xiaofeng, Wu Zhongfu, Yu Juebang.Stability Analyses of Cellular Neural Networks with Continuous Time Delay.Journal of Computational and Applied Mathematics, 2002, 143 (4):29-47.
[68] Liao Xiaofeng, Yu Juebang,Chen Guanrong.Novel Stability Criteria for Bi-directional Associative Memory Neural Networks with Time Delays.International Journal of Circuits Theory and Applications, 2002, 30(5):519-546.
[69] Liao Xiaofeng, Kwok-wo Wong,Wu Zhongfu.Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays . IEEE Transactions on Neural Networks.2003, 14 (1):222-227.
[70] Liao Xiaofeng, Kwok-wo Wong.Global Exponential Stability of Hybrid Bidirectional Associative Memory Neural Networks with Discrete Delays.Physical Review E, 2003, 67, 042901.
[71] Liao Xiaofeng, Wang Jun, Cao Jinde.Global and Robust Stability of Interval Hopfield Neural Networks with Time-varying Delays.International Journal of Neural Systems, 2003, 13 (3):171~182 .
[72] Liao Xiaofeng, Kwok-wo Wong, Yang Shizhong.Convergence dynamics of hybrid bi-directional associtative memory neural networks with distributed delays.Physics Letters A, 2003, 316 (12):55～64 .
[73] Cao Jinde, Wang Jun, Liao Xiaofeng.Novel stability criteria for delayed cellualr neural networks.International Journal of Neural Systems, 2003, 13 (5):367～375.
[74] Liao Xiaofeng, Kwok-wo Wong.Robust Stability of interval bi-directional associative memory neural networks with time delays.IEEE Transactions on SMC-B, 2004, 34 (2):1141～1154.
[75] Liao Xiaofeng, Kwok-wo Wong.Global exponential stability for a class of retarded functional differential equations with applications in neural networks . Journal of Mathematical Analysis and Applications, 2004, 293 (1):125～148.
[76] Liao Xiaofeng,Kwok-wo Wong.Li Chuanguang.Global exponential stability for a class of generalized neural networks with distributed delays.Nonlinear Analysis: Real World Applications, 2004, 5(3):527～547.
[77] Liao Xiaofeng, Kwok-wo Wong,Leung C.Hopf bifurcation and chaos in a single delayed neuron equation with nonmonotonic activation function. Chaos, Solitons & Fractals, 2001, 12(4):1535-1547.
[78] Li Chuandong, Liao Xiaofeng.Global robust stability criteria for interval delayed neural networks via an LMI approach.IEEE Transactions on CAS-II, 2006,53(9):901-905.
[79] Cao Jinde, Wang Jun.Global Asymptotic Stability of a General Class of Recurrent Neural Networks With Time-Varying Delays.IEEE Trans. CAS-I, 2003, 50(1): 34～44.
[80] Liao T.-L.,Wang F.-C..Global stability condition for cellular neural networks with time delay.Electron. Lett.,1999, 35(16):1347～1349.
[81] T.-L. Liao, F.-C. Wang, Global stability for cellular neural networks with time delay.IEEE Trans. on Neural Networks, 2000, 11(6):1481～1484.
[82] Cao Jinde.Global stability conditions for delayed CNNs, IEEE Trans. on CAS-I,2001, 48(11): 1330～1333.
[83] Arik S., Tavsanoglu V..On the global asymptotic stability of delayed cellular neural networks.IEEE Trans. on CAS-I, 2000, 47 (4):571～574.
[84] Arik S. . An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks.IEEE Trans. on Neural Networks, 2002, 13(5):1239～1242.
[85] Arik S.An Improved Global Stability Result for Delayed Cellular Neural Networks.IEEE Trans. on CAS-I, 2002, 49 (8): 1211～1214.
[86] Hale J. K., Lunel S. M. V. . Introduction to the theory of functional differential Equations.Applied mathematical sciences, Vol. 99, New York: Springer, 1999.
[87] Liao X, Mu W, Yu J. Stability analysis of bi-directional association memory with axonal signal transmission delay. Proceedings of the third International Conference on Signal Processing, 1996, 2: 1457-1460.
[88] Liao X, Liu G, YU J. Qualitative analysis of BAM networks. Journal of circuits and systems 1996, 1: 13-18.
[89] Michel, A. N., Farrell, J. A., & Porod, W. Qualitative analysis of neural networks. IEEE Transactions on Circuits Systems I 1989, 36: 229–243.
[90] Gopalsamy K, He X. Delay-dependent stability in bi-directional associative memory networks. IEEE transaction on neural networks 1994; 5:998-1002.
[91] Arik S. Stability analysis of delayed neural networks. IEEE Transaction on circuits and systems 2000, 47(7): 1089-1092.
[92] Cao Jinde. Periodic oscillation and exponential stability of delayed CNN. Physics Letters A 2000, 270: 157–163.
[93] Gopalsamy K., & He XZ. Stability in asymmetric Hopfield networks with transmission delays. Physica D, 1994, 76: 344–358.
[94] Li Chuandong, Liao Xiaofeng, Chen Yong. On the robust stability of bidirectional associative memory neural networks with constant delays. LECTURE NOTES IN COMPUTER SCIENCE 3173: 102-107, 2004.
[95] Joy M. On the global convergence of a class of functional differential equations with application in neural network theory. Journal of Mathematical Analysis and Applications 1999, 232: 61–81.
[96] Joy M. Results concerning the absolute stability of delayed neural networks. Neural Networks 2000, 13: 613–616.
[97] Zhang Y. Global exponential stability and periodic results of delay Hopfield neural networks. International Journal of System Sciences 1996, 27:227-231.
[98] Sanchez E. N., & Perez J. P. Input-to-state stability analysis for dynamic NN. IEEE Transactions on Circuits Systems 1999, 46:1395–1398.
[99] Zhang J. Y. and Yang Y. R., Global stability analysis of bi-directional associative memory neural networks with time delay, Int. J. Circuit Theory and application, 2001, 29(2): 185-196.
[100] Hari Rao V. Sree and Bh, R. M. Phaneendra, Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones, Neural Networks, 1999, 12(3): 455-165.
[101] Li Chuandong, Liao Xiaofeng, Zhang Rong. Delay-dependent exponential stability Analysis of BAM NNs: an LMI approach. Chaos, Solitons & Fractals, 2005, 24(4) 1119-1134.
[102] Arik S. Global robust stability of delayed neural networks. IEEE Trans. CAS-I, 2003, 50 (1): 156-160.
[103] Li Daigao. Matrix theory and its applications. China: Chongqing University Press, 1988.
[104] Arik S. Global asymptotic stability of a larger class of neural networks with constant time delay. Physics Letters A, 2003, 311: 504-511.
[105] Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Physics Letters A, 2002, 297:182-190.
[106] Zhang Q. Global asymptotic stability of Hopfield neural networks with transmission delays. Physics Letters A, 2003, 318: 182-190.
[107] Roska, T., Wu, C. W., Balsi, M. and Chua, L. O. Stability and dynamics of delay-type general neural networks. IEEE Trans. Circuits Syst., 1992, 39(5): 487-490.
[108] L.O. Chua, T. Roska. Stability of a class of nonreciprocal cellular neural networks. IEEE Trans. CAS, 1990, 37(12): 1520-1527.
[109] T. Roska, C.W. Wu, M. Balsi, L.O. Chua. Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans. CAS-I, 1992, 39(6): 487-490.
[110] T. Roska, C.W. Wu, L.O. Chua. Stability of cellular neural networks with dominant nonlinear and delay-type templates, 1993, 40(4): 270-272.
[111] P. P. Civalleri, M. Gilli, L. Pandolfi. On stability of cellular neural networks with delay. IEEE Trans. CAS-I, 1993, 40 (3): 157-165.
[112] M. Gilli. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Trans. CAS-I, 1994, 41(8): 518-528.
[113] Hui Ye, N. Micheal, K. Wang. Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Trans. CAS-I, 1996, 43(7): 532-543.
[114] Y.J. Cao, Q.H. Wu. A note on stability of analog neural networks with time delays. IEEE Trans. Neural networks, 1996, 7(6): 1533-1535.
[115] N. Takashashi. L.O. Chua. On the complete stability of nonsymmetric cellular neural networks. IEEE Trans. CAS-I, 1998, 45(7): 754-758.
[116] Zhi-Hong Guan, G. Chen, Yi Qin. On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans. Neural networks, 2000, 11(2): 534-540,.
[117] Arik S. Global asymptotic stability of a class of dynamical neural networks. IEEE Trans. CAS-I, 2000, 47(4): 568-571.
[118] P. Campolucci, F. Piazza. Intrinsic stability-control method for recursive filters and neural networks. IEEE Trans. CAS-II, 2000, 47(8): 797-802.
[119] J.A.K. Suykens, B. de Moor, J. Vandewalle. Robust local stability of multilayer recurrent neural networks. IEEE Trans. Neural networks, 2000, 11(1): 222-229.
[120] Youshen Xia, Jun Wang. Global exponential stability of recurrent neural networks for solving optimization and related problems. IEEE Trans. Neural networks, 2000, 11(4): 1017-1022.
[121] Xue-Bin Liang, J. Wang. Absolute exponential stability of neural networks with a general class of activation functions. IEEE Trans. CAS-I, 2000, 47(8): 1258-1263.
[122] Xue-Bin Liang. Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons. IEEE Trans. Neural networks, 2000, 11(5): 1194-1196.
[123] X.-B. Liang, Jun Wang. A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case. IEEE Trans. CAS-I, 2000, 47(4): 609-611.
[124] N. Takahashi. A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Trans. CAS-I, 2000, 47(6): 793-799.
[125] Hong Qiao, Jigen Peng, Zong-Ben Xu. Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks. IEEE Trans. Neural networks, 2001, 12(2): 360-370.
[126] Xue-Bin Liang; J. Si. Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. IEEE Trans. Neural networks, 2001, 12(2): 349-359.
[127] Jinde Cao. A set of stability criteria for delayed cellular neural networks. IEEE Trans. CAS-I, 2001, 48(4): 494-498.
[128] Donq Liang Lee. Relaxation of the stability condition of the complex-valued neural networks. IEEE Trans. Neural networks, 2001, 12(5): 1260-1262.
[129] Wen Yu, Xiaoou Li. Some stability properties of dynamic neural networks. IEEE Trans. CAS-I, 2001, 48(2): 256-259.
[130] Xue-Bin Liang, Jun Wang. An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks. IEEE Trans. CAS-I, 2001, 48(11): 1308-1317.
[131] M. Forti. Some extensions of a new method to analyze complete stability of neural networks. IEEE Trans. Neural networks, 2002, 13(5): 1230-1238.
[132] Anping Chen, Jinde Cao, Lihong Huang. An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE Trans. CAS-I, 2002, 49(7): 1028-1032.
[133] Sanqing Hu, Jun Wang. Global stability of a class of continuous-time recurrent neural networks. IEEE Trans. CAS-I, 2002, 49(9): 1334-1347.
[134] Sanqing Hu, Jun Wang. Global stability of a class of discrete-time recurrent neural networks. IEEE Trans. CAS-I, 2002, 49(8): 1104-1117.
[135] Weirui Zhao, Wei Lin, Rongsong Liu, Jiong Ruan. Asymptotical stability in discrete-time neural networks. IEEE Trans. CAS-I, 2002, 49(10): 1516-1520.
[136] Sanqing Hu, Jun Wang. Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks. IEEE Trans. Automatic Control, 2002, 47(5): 802-807.
[137] S. Arik. A note on the global stability of dynamical neural networks. IEEE Trans. CAS-I, 2002, 49(4): 502-504.
[138] Yi Zhang, Pheng Ann Heng, P. Vadakkepat. Absolute periodicity and absolute stability of delayed neural networks. IEEE Trans. CAS-I, 2002, 49(2): 256-261.
[139] Yunong Zhang, Jun Wang. Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment. IEEE Trans. Neural networks, 2002, 13(3): 633-644.
[140] Gwo-Jeng Yu, Chien-Yu Lu, J.S.-H. Tsai, Te-Jen Su, Bin-Da Liu. Stability of cellular neural networks with time-varying delay. IEEE Trans. CAS-I, 2003, 50 (5): 677-678.
[141] Dingguo Chen, R.R. Mohler. Neural-network-based load modeling and its use in voltage stability analysis. IEEE Transactions on Control Systems Technology, 2003, 11(4): 460-470.
[142] A. Meyer-Baese, S.S. Pilyugin, Y. Chen. Global exponential stability of competitive neural networks with different time scales. IEEE Trans. Neural networks, 2003, 14(3): 716-719.
[143] Xuemei Li, Lihong Huang, Jianhong Wu. Further results on the stability of delayed cellular neural networks. IEEE Trans. CAS-I, 2003, 50(9): 1239-1242.
[144] Hong Qiao; Jigen Peng; Xu, Z.-B.; Bo Zhang. A reference model approach to stability analysis of neural networks. IEEE Transactions on Systems, Man and Cybernetics, Part B, 2003, 33 (6): 925-936.
[145] Zhigang Liu, Anping Chen, Jinde Cao, Lihong Huang. Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays. IEEE Trans. CAS-I, 2003, 50 (9): 1162-1173.
[146] Zhigang Zeng, Jun Wang, Xiaoxin Liao. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. CAS-I, 2003, 50(10): 1353-1358.
[147] Qiang Zhang, Runnian Ma, Chao Wang, Jin Xu. On the global stability of delayed neural networks. IEEE Transactions on Automatic Control, 2003, 48(5): 794-797.
[148] Xiao-xin Liao, Jun Wang. Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans. CAS-I, 2003, 50(2): 268-274.
[149] Jiing-Dong Hwang, Feng-Hsiag Hsiao. Stability analysis of neural-network inter-connected systems. IEEE Trans. Neural networks, 2003, 14(1): 201-208.
[150] Sanqing Hu, Jun Wang. Absolute exponential stability of a class of continuous-time recurrent neural networks. IEEE Trans. Neural networks, 2003, 14(1): 35-45.
[151] Jiye Zhang. Globally exponential stability of neural networks with variable delays. IEEE Trans. CAS-I, 2003, 50 (2): 288-290.
[152] V. Singh. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural networks, 2004, 15(1): 223-225.
[153] Haijun Jiang, Zhidong Teng. Boundedness and stability for nonautonomous bidirectional associative neural networks with delay. IEEE Trans. CAS-II, 2004, 51(4): 174-180.
[154] Tianping Chen, Libin Rong. Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural networks, 2004, 15(1): 203-206.
[155] Houduo Qi, Liqun Qi. Deriving sufficient conditions for global asymptotic stability of delayed neural networks via non-smooth analysis. IEEE Trans. Neural networks, 2004, 15(1): 99-101.
[156] Z. Zeng J. Wang, X. Liao. Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. CAS-I, 2004, 50(11): 2313-2324
[157] Junjie Wei, Shigui Ruan. Stability and bifurcation in a neural network model with two delays. Physica D, 1999, 130(3-4): 255-272.
[158] Hongtao Lu. On stability of nonlinear continuous-time neural networks with delays. Neural Networks, 1999, 13(10): 1135-1143.
[159] S. Blythe, Xuerong Mao, Xiaoxin Liao. Stability of stochastic delay neural networks. Journal of The Franklin Institute, 2001, 328(4): 481-495.
[160] Yuming Chen. A remark on ‘On stability of nonlinear continuous-time neural networks with delays. Neural Networks, 2001, 14(10): 1463-1469.
[161] Jigen Peng, Hong Qiao, Zong-ben Xu. A new approach to stability of neural networks with time-varying delays. Neural Networks, 2002, 15(1): 95-103.
[162] Hongyong Zhao. Global stability of bidirectional associative memory neural networks with distributed delays. Physics Letters A, 2002, 297(3-4): 182-190.
[163] He Huang, Jinde Cao, Jun Wang. Global exponential stability and periodic solutions of recurrent neural networks with delays. Physics Letters A, 2002, 298(5-6): 393-404.
[164] Yuming Chen. Global stability of neural networks with distributed delays. Neural Networks, 2002, 15(7): 867-871.
[165] Dongming Zhou, Jinde Cao. Globally exponential stability conditions for cellular neural networks with time-varying delays. Applied Mathematics and Computation, 2002, 131(2-3): 487-496.
[166] Haijun Jiang, Zhiming Li, Zhidong Teng. Boundedness and stability for nonautonomous cellular neural networks with delay. Physics Letters A, 2003, 306(5-6): 313-325.
[167] S. Mohamad, K. Gopalsamy. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation, 2003, 135(15): 17-38.
[168] Bingji Xu, Xinzhi Liu, Xiaoxin Liao. Global asymptotic stability of high-order Hopfield type neural networks with time delays. Computers and Mathematics with Applications, 2003, 45(10-11): 1729-1737.
[169] Xue-Mei Li, Li-Hong Huang, Huiyan Zhu. Global stability of cellular neural networks with constant and variable delays. Nonlinear Analysis, 2003, 53(3-4): 319-333.
[170] Anping Chen, Lihong Huang, Jinde Cao. Existence and stability of almost periodic solution for BAM neural networks with delays. Applied Mathematics and Computation, 2003, 137((1): 177-193.
[171] Boyd S., Ghaoui L.E., Feron E., Balakrishnan V..Linear Matrix Inequalities in system and Control Theory.In:Proceedings of SIAM, Philadephia, 1994.
[172] Kosko, B., Competitive. adaptative bidirectional associative. Memories. Proceedings of the IEEE. First International Conference on Neural Networks, eds M. Cardill and. C. Butter 1988, 2: 759-766
[173] Nesterov, Y., & Nemirovsky, A. Interior point polynomial methods in convex Programming. SIAM: Philadephia PA 1994.
[174] D.Bainov and V. Covachev. Impulsive differential equations with a small parameter. World Scientific, Singapore, 1994.
[175] D. D. Bainov and P.S. Simeonov. Systems with impulse effect: Stability, theory, and applications. Ellis Horwood Limited, Chichester, 1989.
[176] D. D. Bainov and P.S. Simeonov. Impulsive differential equations: Periodic solutions and applications. Longman Group UK Limited, 1993.
[177] A.F.Filippov. Differential equations with discontinuous righthand sides. Mathematics and its applications (Kluwer Academic Publisher). Soviet series. Kluwer Academic, Boston, USA, 1998.
[178] S.G.Pandit and S.G.Deo. Differential systems involving impulses. Springer-Verlag, New York, USA, 1982.
[179] Li ZG, Wen CY, Soh YC. Analysis and design of impulsive control systems. IEEE Trans Automat Contr, 2001, 46 (6): 894-903??.
[180] Lu HT. Chaotic attractors in delayed neural networks. Physics Letters A 2002; 298: 109-116.
[181] S. Arik, V. Tavsanoglu, Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing, 2000, 68: 161-176
[182] J. Cao, Global asymptotics stability of delayed bi-directional associative memory neural networks Appl. Math. Comput. 2003, 142 : 333-339.
[183] Y.H. Xia, J.D. Cao, S.S. Cheng, Global exponential stability of delayed cellular neural networks with impulses, Neurocomputing 2007, 70: 2495-2501..
[184] Z.J. Gui, W.G. Ge, Periodic solutions of nonautonomous cellular neural networks with impulses, Chaos, Solitons and Fractals, 2007, 32: 1760–1771.
[185] Y.X. Wang , W.M. Xiong , Q.Y. Zhou, B. Xiao, Y,H. Yu, Global exponential stability of cellular neural networks with continuously distributed delays and impulses, Physics Letters A, 2006, 350: 89–95.
[186] Z.J. Gui, W.G. Ge, Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses. Physics Letters A, 2006, 354: 84–94.
[187] Y.K. Li, Global exponential stability of BAM neural networks with delays and impulses, Chaos, Solitons and Fractals, 2005, 24(1): 279–285.
[188] Y.K. Li, W.Y. Xing, L.H. Lu Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solution and Fractals, 2006, 27: 437–445.
[189] A. Halanay. Differential equations: Stability, oscillations, time lags. Academic, New York, 1966.
[190] J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A, 2003, 307(2-3): 136-147.
[191] Y.K. Li, L.H. Lu Global exponential stability and existence of periodic solution of Hopfield-type neutral networks with impulses. Phys Lett A, 2004, 333: 51–61.
[192] Z.H. Guan, James L, G. Chen, On impulsive auto-associative neural networks, Neural Networks, 2000, 13: 63–69.
[193] S. Mohamad, K. Gopalsamy, Exponential stability of continuous-time and discrete-time cellular neural networks with delays, Appl.Math. Comput. 2003, 135: 17–38.
[194] A. Chen, J. Cao, L. Huang, Exponential stability of BAM neural networks with transmission delays. Neurocomputing, 2004, 57: 435-454.
[195] Kosko B., Bi-directional associative memory. IEEE transaction on Systems, Man, and Cybernetics 1998, SMC-18: 49-60.
[196] Kosko B., Adaptive Bi-directional associative memories Applied Optics 1989, 26: 4947-4960.
[197] Kosko B., Unsupervised learning in noise. IEEE transaction on neural networks, 1990, NN-1: 44-57.
[198] Kosko B., Structural stability of unsupervised learning in feedback neural networks. IEEE transaction on automatic Control 1991, AC-36: 785-790.
[199] Kosko B., Neural Networks and Fuzzy Systems-A Dynamical System Approach to Machine Intelligence, Prentice-Hall: Englewood Cliffs, NJ, 1992.
[200] Mathai C., Upadhyaya B. C., Performance analysis and application of the Bi-directional associative memory to industrial spectral signatures. Proceeding of IJCNN, ,1989, vol.1: 33-37.
[201] Elsen I., Kraiaiss K.F. and Krumbiegel D., Pixel based 3D object recognition with Bi-directional associative memory. International Conference on neural networks, 1997, 3: 1679-1684.
[202] Maundy B., EI-Masry. A switched capacitor Bi-directional associative memory. IEEE transaction on Circuits and systems 1990, 37(12):1568-1572.
[203] Hasan SMR,Siong NK. A VLSI BAM neural network chip for pattern recognition application. Proceedings of IEEE international Conference on neural networks,1995, vol. 1: 164-168.
[204] K. Gopalsmy, X.Z. He, Delay-independent stability in bidirectional associative memory networks IEEE Trans. Neural Networks, 1994, 5 : 998-1002.
[205] J. Cao, M. Dong, Exponential stability of delayed bi-directional associative memory networks Appl. Math. Comput. 2003, 135: 105-112
[206] J. Cao, L. Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays IEEE Trans. Neural Networks, 2002, 13: 457-463.
[207] S. Haykin, Neural Networks, Prentice Hall, New Jersey, 1999.
[208] S. J. Guo, L.H. Huang, B.X. Dai, Z.Z. Zhang, Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys. Lett. A, 2003, 317: 97-106.
[209] Z. Liu, A. Chen, J. Cao, L. Huang, Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays Phys. Lett. A, 2003, 319: 305-316.
[210] Y.K. Li, P. Liu, Existence and Stability of Positive Periodic Solution for BAM Neural Networks with Delays, Mathematical and Computer Modelling, 2004, 40: 757-770.
[211] T.J.Zhou, A.Chen, ,Y.Y. Zhou, Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays. Physics Letters A, 2005, 343: 336–350.
[212] Q.K. Song, J. Cao, Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction–diffusion terms. Chaos, Solitons and Fractals, 2005, 23: 421–430.
[213] M. Han, P.Bi,, Existence and bifurcation of periodic solutions of high-dimensional delay differential equations. Chaos, Solitons and Fractals, 2004, 20: 1027-1036.
[214] Z. Jin, Z.Ma, M.Han, The existence of periodic solutions of the n-species Lotka–Volterra competition systems with impulsive Chaos, Solitons and Fractals, 2004, 22: 181-188.
[215] Y. K.Li, Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays Chaos, Solitons and Fractals, 2004, 20: 459-466.
[216] X. Liu, G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations, Comput. Math.Appl., 2001, 41: 903–915.
[217] R.E. Gains, Mawhin JL.Coincidence degree and nonlinear differential equation. Berlin: Springer-Verlag, 1977.
[218] J. Dieudonn Foundations of Modern Analysis. Academic Press, New York, MR 1960 ,22:11074.
[219] S. Long and D. Y. Xu. Delay-dependent stability analysis for impulsive neural networks with time varying delays. Neurocomputing (2007), doi: 10.1016/j. neucom. 2007. 03.010. (In press)
[220] Kosko B. A dynamical systems approach to machine intelligence. Neural Networks and Fuzzy Systems, Prentice Hall, New Delhi: Prentice-Hall of India, 1992.
[221] K. Gopalsamy Leakage delays in BAM. J. Math. Anal. Appl., 2007, 325: 1117–1132.
[222] Cao J.D. On exponential stability and periodic solutions of CNNs with delays. Phys. Lett. A, 2000, 267: 312-318.
[223] Chen A.P. & Cao J.D. Almost periodic solution of shunting inhibitory CNNs with delays. Phys. Lett. A, 2000, 298: 161-170.
[224] Huang H. & Cao J.D. Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay. Phys. Lett. A, 2003, 314: 222-231.
[225] Huang H. & Cao J.D. On global asymptotic stability of recurrent neural networks with time-varying delays. Appl. Math. Comput., 2003, 142: 143-154.
[226] Jinling Liang, Jinde Cao. Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays. Physics Letters A, 2003, 314(5-6): 434-442.
[227] Qiang Zhang, Xiaopeng Wei, Jin Xu. Global exponential stability of Hopfield neural networks with continuously distributed delays. Physics Letters A, 2003, 315(6): 431-436.
[228] C. Li, X. Liao, and T. Huang. Exponential stabilization of chaotic systems with delay by periodically intermittent control. CHAOS, 2007,17, 013103, .
[229] S. Mohamad, K. Gopalsamy Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math Comput Simul., 2000, 53: 1–39.
[230] S. Mohamad, K. Gopalsamy Neuronal dynamics in time varying environments: continuous and discrete time models. Discrete Cont Dyn Syst., 2000, 6: 841–860.