时延神经网络系统的Hopf分岔、混沌及其控制研究
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摘要
具有时延的神经网络系统的研究是非线性动力学领域的前沿课题之一。具有时延的动力学系统能更客观地刻划自然界现象的本质，而且具有复杂的动力学行为。本文对一类具有时延的神经元系统的Hopf分岔、混沌现象及其控制问题进行了研究。作者的主要贡献和创新如下：
1．研究了一个带时延的神经元方程，分析相应的线性化方程的超越特征方程，得出系统的线性稳定性和出现Hopf分岔的条件。利用规范形式理论和中心流形定理，解析确定了该时延系统的周期解的稳定性与Hopf分岔方向。该系统中激活函数选取的任意性，为研究其他非单调激活函数的神经元模型提供了一个新的研究方法。
2．将混沌时间序列的预测与改进的Lyapunov指数矩阵计算方法相结合，提出了一种计算最大Lyapunov指数的计算方法，这种方法避免了矩阵算法的优化问题，减少了计算工作量。在此基础上，对具有时延的微分动力系统的LEs问题进行了初步探讨，为时延的微分动力系统LEs估算问题的进一步研究奠定了良好的基础。
3．讨论了非线性动力学系统吸引子的存在性和有界性，根据Hopf分岔定理计算了具有时延的简单神经元方程周期解失稳的参数，用Runge-Kutta方法进行数值仿真，说明具有时延的简单神经元的自治系统能产生混沌现象，即在一阶非线性时延动力学系统中找到了新的混沌发生器，并对二神经元系统进行了相应的分析。
4．介绍了Lyapunov泛函方法的稳定性理论及其在时延神经网络系统中的应用；利用Lyapunov泛函方法，得到了具有混沌现象的带离散时延的简单神经元系统以及二神经元系统的混沌同步的一般化解析条件，避免了计算条件Lyapunov指数，同时也说明无穷维的系统在一定条件下能达到同步。由时延动力学混沌系统维数的无穷性，可望得到更具保密的混沌流。
5．提出并证明了有关具有时延的线性动力学系统的渐近稳定性定理和推论，从而为具有时延的动力学系统提供了一种新的局部稳定性的分析方法；针对具有时延的单神经元系统和二神经元系统，设计了反馈控制模型和基于Washout滤波器的控制模型，并由引进的稳定性定理讨论了控制系统的稳定性，给出了确定控制参数的相关定理；对分岔的反控制问题作了初步探讨，提出了基于Washout滤波器的分岔反控制模型，并进行了理论分析。
6．对一类一阶具有时延的自治连续神经网络系统，采用反馈控制方法，给出了控制系统渐近稳定的解析判别条件的定理；对于参数未知的混沌系统，设计了一种自适应控制模型，并基于Lyapnunov 泛函方法，导出了自适应控制系统渐近稳定的解析判别条件。为研究其他参数未知的混沌系统的控制，提供了一种新的自适应方法。
Researching the problems of neural network system with time-delay is one of the front edge issues in nonlinear dynamics domains. A time-delayed dynamic system having complex dynamic behaviors could depict the essence of nature phenomenon more precisely, and could have The phenomena of the Hopf bifurcation, chaos in a class of time-delayed neural network system and the problems of their control techniques are investigated in this dissertation. The main contributions of the dissertation are as following:
1. A neuron equation with discrete time delay is studied. The conditions of equilibrium stability and Hopf bifurcation for this model are given by analyzing correspond transcendental characteristic equation. The stability of bifurcating periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Since the neuron activation function is considered being arbitrarily, it provides a novel approach to study other delayed neural system with non-increase activation function.
2. An algorithm for determining the largest Lyapunov exponent is developed by combining the predicting chaotic time series and modified matrix method for calculating Lyapunov exponents. This novel algorithm can avoid to solve the optimization problem and reducing the related computations. The problems of LEs of difference differential dynamic system are discussed preliminarily, that has been settled the basic frame for further research of the LLE estimating problems in such systems.
3. The existence and boundary characteristics for attractors of nonlinear dynamic systems are discussed. By applying Hopf bifurcation theorem, the parameters for unstable periodic solution of the simple neuron equation with time-delay are calculated. The results of numerical simulation by Runge-Kutta method show that chaotic phenomenon could be generated in an autonomous system consisting of a simple neuron equation with time-delay. It implies that we can find a new kind of chaotic generators in a first order nonlinear dynamic system with time-delay. The system with two neurons is also discussed.
4. The Lyapunov functional method in stability theory and its application to the neural network system is introduced. By using Lyapunov functional method, we get the general synchronization conditions in analytic form for the chaotic system
consisting of a simple neuron with time-delay. So we can avoid the calculation of the condition Lyapunov exponents. Moreover, we have demonstrated that such a system is with infinite dimension and could be synchronized under certain conditions. It is expected that we can obtain a chaotic flow with much higher cryptic strength in a delayed neural system.
5. The asymptotic stability theorem and relevant corollary for linearized nonlinear dynamic system are presented and proved, upon which a novel method for analyzing local stability of a dynamic system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, we design a feedback control system and a Washout filter based system respectively. By employing the proposed stability theorem, we investigated the stability of a control system and show relevant theorems for choosing parameters of the stabilized control system. A preliminary study for the anti-control problem of bifurcations is also conducted. Washout filter based model is proposed and theoretic analyses are given.
6. A feedback control method is suggested for a class of first order autonomous continuous-time neural network systems. The theorem for asymptotic stability conditions in analytic form of the control system is given. In the case that the parameters of a chaotic system are unknown, we proposed an adaptive control model and asymptotic stability conditions in analytic form of such system is deduced by employing the Lyapunov functional method. The novel adaptive control technique we proposed here also paves a new way to study of other chaotic control system with unknown parameters.
1．研究了一个带时延的神经元方程，分析相应的线性化方程的超越特征方程，得出系统的线性稳定性和出现Hopf分岔的条件。利用规范形式理论和中心流形定理，解析确定了该时延系统的周期解的稳定性与Hopf分岔方向。该系统中激活函数选取的任意性，为研究其他非单调激活函数的神经元模型提供了一个新的研究方法。
2．将混沌时间序列的预测与改进的Lyapunov指数矩阵计算方法相结合，提出了一种计算最大Lyapunov指数的计算方法，这种方法避免了矩阵算法的优化问题，减少了计算工作量。在此基础上，对具有时延的微分动力系统的LEs问题进行了初步探讨，为时延的微分动力系统LEs估算问题的进一步研究奠定了良好的基础。
3．讨论了非线性动力学系统吸引子的存在性和有界性，根据Hopf分岔定理计算了具有时延的简单神经元方程周期解失稳的参数，用Runge-Kutta方法进行数值仿真，说明具有时延的简单神经元的自治系统能产生混沌现象，即在一阶非线性时延动力学系统中找到了新的混沌发生器，并对二神经元系统进行了相应的分析。
4．介绍了Lyapunov泛函方法的稳定性理论及其在时延神经网络系统中的应用；利用Lyapunov泛函方法，得到了具有混沌现象的带离散时延的简单神经元系统以及二神经元系统的混沌同步的一般化解析条件，避免了计算条件Lyapunov指数，同时也说明无穷维的系统在一定条件下能达到同步。由时延动力学混沌系统维数的无穷性，可望得到更具保密的混沌流。
5．提出并证明了有关具有时延的线性动力学系统的渐近稳定性定理和推论，从而为具有时延的动力学系统提供了一种新的局部稳定性的分析方法；针对具有时延的单神经元系统和二神经元系统，设计了反馈控制模型和基于Washout滤波器的控制模型，并由引进的稳定性定理讨论了控制系统的稳定性，给出了确定控制参数的相关定理；对分岔的反控制问题作了初步探讨，提出了基于Washout滤波器的分岔反控制模型，并进行了理论分析。
6．对一类一阶具有时延的自治连续神经网络系统，采用反馈控制方法，给出了控制系统渐近稳定的解析判别条件的定理；对于参数未知的混沌系统，设计了一种自适应控制模型，并基于Lyapnunov 泛函方法，导出了自适应控制系统渐近稳定的解析判别条件。为研究其他参数未知的混沌系统的控制，提供了一种新的自适应方法。
Researching the problems of neural network system with time-delay is one of the front edge issues in nonlinear dynamics domains. A time-delayed dynamic system having complex dynamic behaviors could depict the essence of nature phenomenon more precisely, and could have The phenomena of the Hopf bifurcation, chaos in a class of time-delayed neural network system and the problems of their control techniques are investigated in this dissertation. The main contributions of the dissertation are as following:
1. A neuron equation with discrete time delay is studied. The conditions of equilibrium stability and Hopf bifurcation for this model are given by analyzing correspond transcendental characteristic equation. The stability of bifurcating periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Since the neuron activation function is considered being arbitrarily, it provides a novel approach to study other delayed neural system with non-increase activation function.
2. An algorithm for determining the largest Lyapunov exponent is developed by combining the predicting chaotic time series and modified matrix method for calculating Lyapunov exponents. This novel algorithm can avoid to solve the optimization problem and reducing the related computations. The problems of LEs of difference differential dynamic system are discussed preliminarily, that has been settled the basic frame for further research of the LLE estimating problems in such systems.
3. The existence and boundary characteristics for attractors of nonlinear dynamic systems are discussed. By applying Hopf bifurcation theorem, the parameters for unstable periodic solution of the simple neuron equation with time-delay are calculated. The results of numerical simulation by Runge-Kutta method show that chaotic phenomenon could be generated in an autonomous system consisting of a simple neuron equation with time-delay. It implies that we can find a new kind of chaotic generators in a first order nonlinear dynamic system with time-delay. The system with two neurons is also discussed.
4. The Lyapunov functional method in stability theory and its application to the neural network system is introduced. By using Lyapunov functional method, we get the general synchronization conditions in analytic form for the chaotic system
consisting of a simple neuron with time-delay. So we can avoid the calculation of the condition Lyapunov exponents. Moreover, we have demonstrated that such a system is with infinite dimension and could be synchronized under certain conditions. It is expected that we can obtain a chaotic flow with much higher cryptic strength in a delayed neural system.
5. The asymptotic stability theorem and relevant corollary for linearized nonlinear dynamic system are presented and proved, upon which a novel method for analyzing local stability of a dynamic system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, we design a feedback control system and a Washout filter based system respectively. By employing the proposed stability theorem, we investigated the stability of a control system and show relevant theorems for choosing parameters of the stabilized control system. A preliminary study for the anti-control problem of bifurcations is also conducted. Washout filter based model is proposed and theoretic analyses are given.
6. A feedback control method is suggested for a class of first order autonomous continuous-time neural network systems. The theorem for asymptotic stability conditions in analytic form of the control system is given. In the case that the parameters of a chaotic system are unknown, we proposed an adaptive control model and asymptotic stability conditions in analytic form of such system is deduced by employing the Lyapunov functional method. The novel adaptive control technique we proposed here also paves a new way to study of other chaotic control system with unknown parameters.
引文
[1] Yang Kuang，Delay Differential Equations, Academic Press, Inc. London. 1993.
[2] Xiaofeng Liao, Kwok-Wo Wong, Zhongfu Wu, and Guanrong Chen. Novel Robust Stability Criteria for interval-Delayed Hopfield Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 2001, 48(11):1355-1359.
[3] 张锦炎，冯贝叶. 常微分方程几何理论与分支问题. 北京大学出版社，北京，2000年.
[4] Xiaofeng Liao, Zhongfu, and Juebang Yu, Hopf bifurcation analysis of a neural system with a continuously distributed delay, International Symposium on Signal Processing and Intelligent System, Guangzhou ,China ,Nov. 1999. P.546-549.
[5] Xiaofeng Liao, Zhongfu and Juebang Yu, Stability switches and bifurcation analysis of a neural network with continuously distributed delay, IEEE Trans. On SMC-I, 1999,29(6),692-696.
[6] K. Gopalsamy, I. Leung, Delay induced periodicity in a neural network of excitation and inhibition, Physica D, 89(1996),395-426.
[7] 廖晓峰，吴中福，虞厥邦，带分布时延神经网络：从稳定到振荡再到稳定的动力学现象，电子与信息学报， 2001, 23(7):689-692.
[8] Xiaofeng Liao, Kwok-wo Wong, Zhongfu Wu, Bifurcation analysis in a two-neuron system with continuously distributed delays. Physica D, 2001,179(1/2): 123-141.
[9] 靳 藩编著. 神经计算智能基础. 西南交通大学出版社, 成都, 2000年.
[10] K. Murali, M. Lakshmanan, and L. O. Chua. The Simplest Dissipative Nonautonomous Chaotic Circuit. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1994, 41(6):462-463.
[11] Hongtao Lu, Yongbao He, and Zhenya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1998, 45(2):178-181.
[12] Marco Gilli. Strange Attractors in Delayed Cellular Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1993, 40(11):849-853.
[13] Hongtao Lu and Zhenya He. Chaotic Behavior in First-Order Autonomous Continuous-Time Systems with Delay. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1996, 43(8):699-702.
[14] K. Gopalsamy and Issic K. C. Leung. Convergence under Dynamical Thresholds with Delay. IEEE Trans. on Neural Networks. 1997, 8(2):341-348.
[15] J. Belair, S. Dufour, Stability in a three-dimensional system of delay-differential equations, Can. Appl. Math. Quart. , 1996,4(2),135-156.
[16] L. Olien, J. Belair, Bifurcations, stability and monotonicity properties of a delayed neural network model", Physica D, 102(1997), 349-363.
[17] 周尚波，廖晓峰，虞厥邦. 具有任意激活函数的时延神经元方程的Hopf 分岔，电子科学学刊.
[18] Hongtao Lu and Zhengya He. Chaotic Behavior in first-order Autonomous Continuous-time systems with delay. IEEE trans. on CAS-1, 1996, .43(8):700-702.
[19] Xin Wang. Period-Doubling to Chaos in A Simple Neural Network. Neural Networks, IJCNN-91-Seattle International Joint Conference on, 1991, Vol.2, pp:333-339.
[20] Li XIE, Xing HE, Weidong ZHANG, Xiaoming XU. Single Chaotic Neuron with Time-Delay. Circuits and Systems, IEEE APCCAS 2000, the 2000 IEEE Asia-pacific Conference on, pp.809-812.
[21] Yu-Chu Tian and Furong Gao. Simple Delay Systems with Chaotic Dynamics. Control of Oscillations and Chaos, 1997, Proceedings, 1997 1st International Conference, Vol.2, pp.319-320.
[22] Hongtao Lu, Yongbao He, and Zhengya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks. IEEE trans. on CAS-1, 1996, 45(2):178-181.
[23] Givalleri P P.. Gilli M. and L. Pandolfi. On stability of cellular neural networks with delay. IEEE trans. on CAS, 1993, 40(3):157-165
[24] J. Cao. Global stability analysis in delayed cellular neural networks. Phys. Rev. E. 59(1999):5940-5944.
[25] S. Arik and V. Tavanoglu. On the global symptotic stability of delayed cellular neural networks. IEEE trans. on CAS-1, 47:571-574, 2000.
[26] J. Cao. Periodic solutions and exponential stability in delayed cellular neural networks. Phys. Rew. E, 60(1999):3244-3248.
[27] J. Cao.On stability of delayed cellular neural networks. Phys. Lett. A, 261(1999):303-308.
[28] T. Roska, C. W. Wu and L. O. Chua. Stability of cellular neural networks with dominant nonlinear and delay-type template, IEEE trans. on CAS-1, 1993, 40:270-272.
[29] T. Roska, C. W. Wu, M. Balsi and L. O. Chua. Stabilty and dynamics of delay-type general and cellular neural networks. IEEE trans. on CAS-1, 1992, 39:487-490.
[30] M. Gilli. Stability of cellular neural networks and delayed cellular neural networks with nonpostive template and nonmononic output functions. IEEE trans. on CAS-1, 1999, 41:518-528.
[31] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs. IEEE trans. on CAS-1, 45:168-171, 1998.
[32] S. Arik and V. Tavsanoglu. On the global asymptotic stability of delayed cellular neural networks. IEEE trans. on CAS-1, 2000, 47:571-574.
[33] Xiaofeng Liao, Kwok-Wo Wong, Juebang Yu. Novel Stability conditions for Cellular Neural Networks with Time Delay. International Journal of Bifurcation and Chaos. 2000, 11(7):1853-1864.
[34] Liaofeng Liao and Juebang Yu. Robust Stability for Interval Hopfield Neural Network with Time Delay. IEEE Trans. on Neural Network. 1998, 9(5):1042-1045.
[35] P. Celka. Chaotic Synchronization and Moduluation of Nonlinear Time-Feedback Optical Systems. IEEE Trans. on CAS-Ⅰ:Fundamental Theory and Applications, 1995,42(8):455-463.
[36] A.Londei, C.Mazio. A Controlled Chaotic Neural Network for Storing and Retriving Information. CNNA'96:Fourth IEEE international workshop Neural Network and their Applications. Sevitte, Spain, June 24-26, 1996, pp.51-56.
[37] Yang Biao, Kuang Jiaoxun. The PmL-stability of Implicit Runge-Kutta Methods for Delay Differential Equations. J. of Shanghai Teachers Univ.(Natural Science), 28(1):8-15, 1999.
[38] 丛玉豪，匡蛟勋. 数值求解时延微分的步长准则. 计算数学, 23(2):139-144, 2001
[39] 杨维明编著，时空混沌和耦合映象格子，上海科技教育出版社，上海，1994.
[40] 王炎，廖晓峰，吴中福，虞厥邦，一个带时延神经网络的分岔现象研究，电子科学学刊， 2000, 22(7):972-977.
[41] 周作领，符号动力系统，上海科技出版社，1997.
[42] Harold Szu,Richard Yentis C. Charies C. el. at.. Chaotic Neural Models and Artificial Networks. Proceedings of 1993 International Joint Conference on Neural Networks. Pp. 1473-1476.
[43] Kevin Judd and Kazuyuki Aihara. Neural Network and Chaos. 1992 IEEE International Symposium on Circuit and Systems, 6(1992):2765-2768.
[44] Yuyao He, Lipo Wang. Chaotic Neural Networks and Their Applications. Proceedings of 3rd World Congress on Intelligent Control and Automation. 2000, pp. 826-830.
[45] Zou F, Nossek J A. Bifurcation and chaos in cellular neural networks. IEEE Circuits and Systems. 1993, 40 (3):341-348.
[46] Andrew M.Fraser. Information and Entropy in Strange Attactors. IEEE Trans. on information theory. 1989, 35(2):245-262.
[47] D.Ruelle. Ergodic Theory of chaos and strange attractors. Rew. Mod. Phys. 1985, 57(3-4): 617-1115
[48] Ippei Shimada and Tomomasa Nagashima. A Numerical Approach to Erogodic Problem of Dissipative Dynamical Systems. Progress of Theoretical Physics, 1979, 61(6): 1605-1616
[49] Thomas S. Parker, Leon O. Chua. Practical Numerical Algorithms for Chaotic Systems. Springer_Verlag, World Publishing Corp. 1992.
[50] Yuquan He, Ruidong Chi and Naiwen He. Lyapunov exponents of the circle map in human hearts. Phys. Lett. A, 170(1992):29-32.
[51] X. Zeng, R. Eykholt, and R. A. Pielke. Estimating the Lyapunov-Exponent Spectrum from Short Time Series of Low Precision. Phys. Rev. Lett. 1991,66(25):3229-3232.
Di He, Cheb He, Ling-go Jiang, Hong-wen Zhu, and Guang-rui Hu. Chaotic Characteristic of a One-Dimensional Iterative Map with Infinite Collapses. IEEE Trans. on CAS-I:
[52] Fundamental Theory and Applications, 2001, 48(7):900-906.
[53] 马军海, 陈予恕,刘曾荣, 动力系统实测数据的Lyapunov指数的矩阵算法, 应用数学与力学, 1999，20(9):919-927.
[54] 杨绍清. 一种最大李雅普诺夫指数估计的稳健算法, 物理学报, 2000, 49(04):636-640.
[55] Yan Hong Lim, David C. Hamill. Problem of Computing Lyapunov Exponents In Power Electronics. Circuits and Systems, ISCAS'99, 1999, 5(5):297-301.
[56] Holger Kantz. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A, 185(1994):77-87.
[57] Keith Briggs. An improved method for estimating Liapunov exponents of chaotic time series. Phys. Lett. A, 1990,151(1,2):27-32.
[58] 陈关荣. 控制动力学系统的分岔现象. 控制理论与应用, 2001, 18(2):153-159
[59] Xiao Fan Wang, Guanrong Chen. Controlling bifurcating dynamics via chaotification. Decision and Control, Proceedings of the 40th IEEE Conf. on , 2001, 1: 692 -697.
[60] Sang-Ho Lee. Jong-Keun Park, Byung-Ha Lee. A study on the nonlinear controller to prevent unstable Hopf bifurcation. Power Engineering Society Summer Meeting, 2001 ,2: 978 -982.
[61] Wang Y. Bifurcation control in systems governed by functional differential equations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 5: 4409 -4414.
[62] Alonso, D.; Paolini, E.; Moiola, J. On anticontrol of Hopf bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3 : 2072 -2077.
[63] MingQing Xiao, Wei Kang. Feedback control of Hopf bifurcations via integral averaging method. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3: 2066 -2071.
[64] Guanrong Chen, Yap, K.C. Jialiang Lu Feedback control of Hopf bifurcations. Circuits and Systems, SCAS '98. Proceedings of the 1998 IEEE International Symposium on ,3: 639 -642.
[65] Wang, Y. Murray R.M. Feedback stabilization of steady-state and Hopf bifurcations. Decision and Control, Proceedings of the 37th IEEE Conf. on , 1998, 3: 2431 -2437.
[66] Moiola, J.L., Berns, D.W., Guanrong Chen Feedback control of limit cycle amplitudes. Decision and Control, Proceedings of the 36th IEEE Conf. on , 1997, 2: 1479 -1485.
[67] Nakajima, H., Ueda Y. On the stability of delayed feedback control of chaos. Control of Oscillations and Chaos, Proceedings., 1st International Conf. , 1997, 3: 411 -414.
[68] Moiola, J.L., Chen G. Hopf bifurcations in time-delayed nonlinear feedback control systems. Decision and Control, Proceedings of the 34th IEEE Conf. on , 1995, 1: 942 -948.
[69] Genesio, R., Tesi A., Wang H.O., Abed E.H. Control of period doubling bifurcations using harmonic balance. Decision and Control, Proceedings of the 32nd IEEE Conf. on , 1993. 1: 492 -497.
[70] Colonius F., Hackl G., Kliemann W. Controllability near a Hopf bifurcation. Decision and Control, Proceedings of the 31st IEEE Conf. on , 1992, 2: 2113 -2118.
[71] Nakajima H. Ueda Y. On the stability of delayed feedback control of chaos. Control of Oscillations and Chaos, Proceedings., 1st International Conf. , 1997, 3: 411 -414.
[72] Moiola J.L., Chen G. Hopf bifurcations in time-delayed nonlinear feedback control systems. Decision and Control, Proceedings of the 34th IEEE Conf. on , 1995, 1:942 -948 .
[73] Alonso D., Paolini E., Moiola J. On anticontrol of Hopf bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3: 2072 -2077.
[74] MingQing Xiao, Wei Kang. Feedback control of Hopf bifurcations via integral averaging method. Decision and Control, Proceedings of the 39th IEEE Conf. on, 2000, 3: 2066 -2071.
[75] Juan Li, Venkatasubramanian V. Study of Hopf bifurcations in a simple power system model. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 4: 3075 -3079.
[76] Hamzi B., Kang W., Barbot J.-P. On the control of Hopf bifurcations.Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 2: 1631 -1636.
[77] Hua O. Wang, Dong S. Chen, Bushnell L.G. Dynamic feedback control of bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 2: 1619 -1624.
[78] Chang D.-E., Kang W., Krener A.J. Normal forms and bifurcations of control systems. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000 , 2: 1602 -1607.
[79] D'Amico, M.B., Moiola, J.L., Paolini E.E. Hopf bifurcation in discrete-time systems via a frequency domain approach. Control of Oscillations and Chaos, 2000. Proceedings. 2nd International Conf. , 2000, 2: 290 -293.
[80] Tomashevskiy, A.I.; Kapranov, M.V. Bifurcations and chaos in amplifier phase control systems. Control of Oscillations and Chaos, Proceedings. 2nd International Conf. , 2000, 3: 530 -535 .
[81] 刘向东. Hopf分岔方向控制的频域方法. 非线性动力学学报, 1998, 5(1):69-74.
[82] Dong Chen; Wang H.O.; Guanrong. Chen Anti-control of Hopf bifurcations through washout filters. Decision and Control, Proceedings of the 37th IEEE Conf. on , 1998, 3: 3040 -3045.
[83] Lerm, A.A.P. Control of hopf bifurcation in power systems via a generation redispatch. Power Tech Proceedings, IEEE Porto , 2001,2: 6-10.
[84] 方锦清. 非线性系统中混沌的控制与同步及其应用前景(一)[J]. 物理学进展，1996，16(1):1-7.
[85] 方锦清. 非线性系统中混沌的控制方法、同步原理及其应用前景(二)[J]. 物理学进展，1996，16(2):137-202.
[86] Pecora M., Carroll L. Synchronization in Chaotic System. Phys. Rev. Lett., 1990, 65(8):821-823.
[87] Pecora M., Carroll L. Driving System with Chaotic System. Phys. Rev. Lett., 1991, 44(4):2374-2383.
[88] Macief. Oyorzalek, Taming Chaos: Part II ? Control, IEEE Trans. Circuits syst.-1, 1993， 40(10) :693-699.
[89] 禹思敏, 丘水生. 混沌系统及混沌神经网络同步的研究. 广东工业大学学报, 2000, 17(4):1-5.
[90] Shinbrot T., Grbogi C., Ott E., Yorke J. A., Using small perturbations to control chaos[J], Nature, 1993, 363:411-417.
[91] Tetsuro Eudo and Leo O. Chua. Synchronization of Chaos in Phase-Locked Loops. IEEE Trans. on CAS. 1991, 38(12): 1580-1588.
[92] Edgar N. Sanchez, Jose P. Perez, Luis J. Ricalde et al. Chaos Synchronization Via Adaptive Recurrent Neural Control. Proceedings of the 40th IEEE Conference on Decision and Control 2001,ThP07-3:3536-3539.
[93] 李兵, 蒋蔚孙. 混沌优化方法及其应用. 控制理论与应用, 1997, 14(4): 613-615.
[94] 王光瑞，于熙龄，陈式刚编著，混沌的控制、同步与利用，国防工业出版社，2001.
[95] Edward Ott, Celso Drebogi, and James A. Yorke. Controlling Chaos. Phys. Rev. Lett. 1990, 64(11): 1196-1199.
[96] Yueming Zeng, Sahjendra N. Singh. Adaptive Control of Chaos in Lorenz System. Dynamics and Control. 7(1997):143-154.
[97] Guangrong Chen. Chaos: Control and Anti-Control. IEEE Circuits and Systems. 1998, 9 (1):3-6.
[98] Nigel Grook and Tjeerd Olde Scheper. An adaptive Chaotic Neural Network. Proceedings of the 2002 International Joint Conference, 2002, Vol.3, pp.2580-2585.
[99] A. Yu, Markov, A. L. Fradkov, G. S. Simin. Adaptive Synchronization of Chaotic Generators Based on Tunnel Diodes. Proceedings of the 35th Conference on Decision and Control. Kobe, Japan., December 1996.
[100] 钟国群，蔡氏电路混沌同步保密通讯，电路与系统学报，1996，1（1）
[101] 周尚波, 何松柏,虞厥邦,廖晓峰.用于保密通信的混沌跳频序列. 信号处理,2001,17(增刊):9-12.
[102] 何松柏,周尚波.一种用于混沌通信的跳频合成器设计.系统工程与电子技术，2002,24(3):11-13.
[103] 何松柏,王琪贤,周尚波.混沌无线通信研究. 信号处理, 2001,17(增刊):5-6.
[104] Veliko Milanovic and Mona E. Zaghloul. Synchronization of Chaotic Neural Networks for Secure Communictions.
[105] L.Kocarev, K.S.Halle and L.O.Chua. Experimental Demonstration of secure Communication via Chaotic Synchronization. Int. J. of Bifurcation and Chaos. 2(1992):709-713.
[106] Y.Horio and K.Suyama. Experimental Verification of Signal Transmission Using Synchronized SC Chaotic Neural Networks. IEEE Tran. CAS I, 1995,42(7):393-395.
[107] 李忠，毛宗源，混沌控制综述，电路与系统学报，1998，3（1）：59-65.
陈德钊，董军，胡上序，混沌动力学在智能信息处理中的应用研究现状，计算机科学，
[108] Vol.25, No.3 1998
[109] Kazuo Tanaka, Takayuki Ikeda, and Hua O. Wang, A unified Approach to controlling Chaos via an LMI-Based Fuzzy Control System Design, IEEE Trans. Circuits Syst.-1, 1998, 45(10):
[110] 夏承铨，三阶非自治电路中的混沌振荡，电路与系统学报，Vol.1, No.2, 1996
[111] Yao Y, Freeman W. J.Model of biological pattern recognition with spatially dynamics. Neural Networks, 1990,3:153-170.
[112] 陆燕，杜继宏，李春文，延时时间未知的时延系统神经网络补偿控制，清华大学学报(自然科学版)，1998，38(9):67-69.
[113] Sitte R.,Sitte J. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series. IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2000,30(4): 568 -572.
[114] Ming-Hsuan Yang, Ahuja N., Tabb M..Extraction of 2D motion trajectories and its application to hand gesture recognition., IEEE Trans. on Pattern Analysis and Machine Intelligence. 2002, 24(8) :1061 -1074.
[115] Hirasawa K, Murata J, Jinglu Hu, Chunzhi Jin. Universal learning network and its application to robust control. IEEE Trans. on Systems, Man and Cybernetics, Part B, 2000，30(3): 419 -430.
[116] Li Xinhong, Wang Shaobo. Adaptive PIP controller based on neural network for time-delay systems and its applications. Int. Conf. on Info-tech and Info-net Proceedings. 4(2001 ):346 -351.
[117] Woods, W.P.; Johnson, S.R. Comparison of the response of a time delay neural network with an analytic model. Proceedings of the 2002 Int. Joint Conf. on Neural Networks, 2002, vol.2, pp.1120-1125.
[118] Sitte R, Sitte J.. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series ., IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews , 2000, 30(4 ):568 -572.
[119] Sick B. Online tool wear monitoring in turning using time-delay neural networks. Proceedings of the 1998 IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 1998, Volume: 1 .pp:445 -448.
[120] Ning Lan, Hua-Quan Feng, Crago P.E. Neural network generation of muscle stimulation patterns for control of arm movements. IEEE Trans. on Neural Systems and Rehabilitation Engineering, 1994,2(4):213 -224.
[121] Wang X. Text-Dependent speaker verification using recurrent time delay neural networks for feature extraction . Neural Networks for Processing [1993] III. Proceedings of the 1993 IEEE-SP Workshop , 1993, pp:353 -361.
[122] Fang Y.H., Yagoub M.C.E., Wang F., Zhang Q.J. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks. Microwave Symposium Digest. 2000 IEEE MTT-S International, Volume: 2, pp. 883 -886.
[123] Yonghua Fang, Yagoub M.C.E.,Fang Wang, Qi-Jun Zhang. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks., IEEE Transactions on Microwave Theory and Techniques, 48(12): 2335 -2344.
[124] Nakagawa S., Hirata Y. Comparison among time-delay neural networks, LVQ2 discrete parameter HMM and continuous parameter HMM. 1990, vol.1, pp.509 -512.
[125] Waibel A., Hanazawa T., Hinton G., Shikano K., Lang K. Phoneme recognition: neural networks vs. hidden Markov models vs. hidden Markov models. Int. Conf. on Acoustics, Speech, and Signal Processing, 1988, vol.1, pp.107 -110.
[126] Dugast C., Devillers L. Incorporating acoustic-phonetic knowledge in hybrid TDNN/HMM frameworks. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992, Volume: 1, pp.421 -424.
[127] Oweiss K., Abdel Alim O. Performance evaluation of time-delay fuzzy neural networks for isolated word recognition. Int. Symposium on Neuro-Fuzzy Systems, 1996, pp.203 -211.
[128] Mastorocostas P., Theocharis J.B. A generalized TSK dynamic fuzzy neural network: application to adaptive noise cancellation. The Ninth IEEE International Conference on Fuzzy Systems, 2000,Volume:2, pp.877 -882.
[129] Tan C.X., Tachibana H..Nonlinearity-tolerated active noise control using an artificial neural network. IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics, 1997,vol.4,pp.19-22.
[130] Thyssen J., Nielsen H., Hansen S.D. Non-linear short-term prediction in speech coding. 1994. ICASSP-94., 1:185 -188.
[131] Sitte R., Sitte J. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series. IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2000, 30(4):568 -572.
[132] Yu D.L., Williams D., Gomm J.B. On-line implementation of a model predictive controller on a multivariable chemical process. Model Predictive Control: Techniques and Applications - Day 2 (Ref. No. 1999/096), IEE Two-Day Workshop on , 1999, 2:1 -5.
[133] Gatt, E., Micallef, J., Micallef, P., Chilton, E. Phoneme classification in hardware implemented neural networks., The 8th IEEE Int. Conf. on Electronics, Circuits and Systems, 2001, Volume: 1, pp.481 -484.
[134] Jedra, M., El Khattabi, N., Limouri, M., Essaid A. Recognition of seed varieties using neural networks analysis of electrophoretic images., Proceedings of the IEEE-INNS-ENNS Int. Joint Conf. on Neural Networks, 2000, Volume: 5, pp.521 -526.
[135] Gatt, E., Micallef, J., Chilton, E. An analog VLSI time-delay neural network implementation for phoneme recognition. Proceedings of the 2000 6th IEEE Int. Workshop on Cellular Neural Networks and Their Applications, 2000 ,pp.315 -320.
Jiang Minghu, Yuan Baozong, Tang Xiaofang, Lin Biqin. Fast learning algorithms for time-delay neural networks phoneme recognition. The Fourth Int. Conf. on Signal
[136] Processing Proceedings, 1998 , vol.1. pp.730 -733 .
[137] Selouani S.-A., Caelen, J. Arabic phonetic features recognition using modular connectionist architectures. IEEE 4th Workshop on Interactive Voice Technology for Telecommunications Applications, 1998. Proceedings. Pp.155 -160.
[138] Hui W.M., Liu P.C.K., Li K.C. Cantonese phonemes recognition using modular neural network approach. IEEE Int. Symposium on Information Theory Proceedings, 1997, pp. 210.
[139] Islam, R., Hiroshige, M., Miyanaga, Y., Tochinai, K. Phoneme recognition using modified TDNN and a self-organizing clustering network. IEEE Int. Symposium on Circuits and Systems, 1995 , Volume: 3, pp.1816 -1819.
[140] Duanpei Wu, Gowdy J.N. Tunable time delay neural networks for isolated word recognition. Southeastcon '95. Visualize the Future., Proceedings., IEEE , 1995 ,pp.220 -223.
[141] Dugast C., Devillers L., Aubert, X. Combining TDNN and HMM in a hybrid system for improved continuous-speech recognition. IEEE Trans. on Speech and Audio Processing, 1994, Part: 2 , 2(1):217 -223.
[142] Minh Tue Vo. Incremental learning using the time delay neural network. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 1994, II: 629 -632.
[143] Berthold M.R. A time delay radial basis function network for phoneme recognition. Neural Networks, 1994. IEEE World Congress on Computational Intelligence., 1994 IEEE Int. Conf. on , 1994, 7: 4470 -4472.
[144] Weber, D.M. Parallel implementation of time delay neural networks for phoneme recognition. EEE International Conference on Neural Networks, 1993, vol.3, pp.1583 -1587.
[145] Jang C.S., Un C.K. Integrating time-delay neural networks and fuzzy HMM for phoneme-based word recognition. Electronics Letters, 1992, 28(25):2319 -2320.
[146] Wendell T.C., Abdelhamied K. A phoneme recognition system using modular construction of time-delay neural networks. Proceedings., Fifth Annual IEEE Symposium on Computer-Based Medical Systems, 1992, pp.704 -709.
[147] Takami J., Kai A., Sagayama S. Speech recognition by combining pair wise discriminant time-delay neural networks and predictive LR-parser. Neural Networks for Signal Processing, Proceedings of the 1991 IEEE Workshop, pp.327 -336.
[148] Sugiyama M., Sawai H., Waibel A.H. Review of TDNN (time delay neural network) architectures for speech recognition. IEEE Int. Symposium on Circuits and Systems, 1991, vol.1, pp.582 -585.
[149] Bennani Y., Chaourar N., Gallinari P., Mellouk A. Validation of neural net architectures on speech recognition tasks. Int. Conf. on Acoustics, Speech, and Signal Processing, vol.1, pp. 97 -100.
Bimbot F., Chollet G., Tubach, J.-P. TDNNs for phonetic features extraction: a visual
[150] exploration, Int. Conf. on Acoustics, Speech, and Signal Processing, 1991, vol.1,pp.73 -76.
[151] Sawai H. TDNN-LR continuous speech recognition system using adaptive incremental TDNN training, International Conference on Acoustics, Speech, and Signal Processing, 1991, vol.1, pp. 53 -56
[152] Sawai H. Frequency-time-shift-invariant time-delay neural networks for robust continuous speech recognition. 1991, vol.1, pp. 45 -48.
[153] Hampshire J.B. Waibel A.H. A novel objective function for improved phoneme recognition using time-delay neural networks. IEEE Trans. on Neural Networks, 1990, 1(2):216 -228.
[154] Kiseok Kim, Inbum Kim, Heeyeung Hwang. A study on the recognition of the Korean monothongs using artificial neural net models. Information Technology, 1990. 'Next Decade in Information Technology', Proceedings of the 5th Jerusalem Conference on (Cat. No.90TH0326-9) , 1990, pp.364 -371.
[155] Shaw A., Mitchell R.A. Phoneme recognition with a time-delay neural network. Neural Networks, 1990., 1990 IJCNN Int. Joint Conf. on , 1990, vol.2, pp.191 -195.
[156] Ma W., Van Compernolle D. TDNN labeling for a HMM recognizer. Acoustics, Speech, and Signal Processing, 1990 Int. Conf. on , 1990, vol.1, pp.421 -423.
[157] Hampshire J.B., Waibel A.H. The Meta-Pi network: connectionist rapid adaptation for high-performance multi-speaker phoneme recognition. Int. Conf. on Acoustics, Speech, and Signal Processing , 1990, vol.1, pp.165 -168.
[158] Hampshire J.B., Waibel A.H. A n_ovel objective function for improved phoneme recognition using time delay neural networks. Int. Joint Conf. on , 1989, vol.1, pp. 235 -241.
[159] Waibel A, Sawai H., Shikano K. Consonant recognition by modular construction of large phonemic time-delay neural networks. Int. Conf. on Acoustics, Speech, and Signal Processing, 1989, vol.1, pp.112 -115.
[160] Rivlin Z. Telephones you can talk to. IEEE Potentials , 1989, 8(4): 13 -16.
[161] Waibel A., Hanazawa T., Hinton G., Shikano K., Lang K.J. Phoneme recognition using time-delay neural networks. IEEE Trans. on Acoustics, Speech and Signal Processing, 37(3): 328 -339.
[162] Jiang Minghu, Zhu Xiaoyan. A novel fast learning algorithms for time-delay neural networks.Int. Joint Conf. on Neural Networks, 1999, Volume: 2, pp.1380 -1383.
[163] Sawai H., Waibel A., Miyatake M., Shikano K. Spotting Japanese CV-syllables and phonemes using the time-delay neural networks. Int. Conf. on Acoustics, Speech, and Signal Processing, 1989. vol.1, pp.25 -28 .
[164] Sawai H., Waibei A., Haffner P. et al. Parallelism, hierarchy, scaling in time-delay neural networks for spotting Japanese phonemes CV-syllables., Int. Joint Conf. on Neural Networks, 1989, vol.2, pp.81 -88.
[165] Miyatake M., Sawai H., Minami Y., Shikano K. Integrated training for spotting Japanese phonemes using large phonemic time-delay neural networks. Acoustics, Speech, and Signal Processing, Int. Conf. on , 1990, vol.1, pp. 449 -452.
[166] Lavagetto F. Time-delay neural networks for estimating lip movements from speech analysis: a useful tool in audio-video synchronization. IEEE Trans. on Circuits and Systems for Video Technology, 1997 , 7(5): 786 -800.
[167] Lavagetto F, Lepsoy S, Braccini C, Curinga S. Lip motion modeling and speech driven estimation. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 1997 , Volume: 1 , pp.183 -186.
[168] Kiseok Kim, Inbum Kim, Heeyeung Hwang. A study on the recognition of the Korean monothongs using artificial neural net models. Information Technology, 1990. 'Next Decade in Information Technology', Proceedings of the 5th Jerusalem Conf. on (Cat. No.90TH0326-9) , 1990,pp.364 -371.
[169] Coggins K.M., Pricipe J. Detection and classification of insect sounds in a grain silo using a neural network. Proceedings of IEEE Int. Joint Conf. on Neural Networks,1998 , Volume: 3 , pp.1760 -1765.
[170] 钟林,刘润生 . 新神经网络结构及其在数码语音识别中的应用. 清华大学学报(自然科学版)，2000，40（3）:27-32.
[171] Mingyu Li, Shangbo Zhou , Songbai He, Juebang Yu Radial Basis Function Neural Networks Models for Power-Amplifier Design, to be submitted.
[172] Y onghua Fang, Yagoub, M.C.E, Fang Wang, and Qi-Jun Zhang. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks", IEEE Trans. Microwave theory Tech, 2000, 48(12):2335-2344.
[173] 肖怀铁,付强,庄钊文等,宽带毫米波雷达目标时延神经网络识别新方法. 红外与毫米波学报，2001，20（6）：459-463.
[174] Shi K.L. et Al., Direct self control of induction motor based on neural network. Industry Applications, IEEE Trans. on , 2001, 37(5):1290 -1298.
[175] Kurita Y., Hashimoto T., Ishida Y. An application of time delay estimation by ANNs to frequency domain adaptive I-PD controller. Int. Joint Conf. On Neural Networks, 1999, Volume: 3 , pp.2164 -2167.
[176] Balestrino A., Verona F.B., Landi A. Online process estimation by ANNs and Smith controller design. Control Theory and Applications, IEE Proceedings- , 1998, 145 (2): 231 -235.
[177] Zhang Shu-Ling, Xie Ke-ming. The intelligent learning control using single neuron and its application in an industrial boiler. IEEE Int. Conf. on Intelligent Processing Systems. 1997, Volume: 1 , pp. 797 -800.
[178] 钟晓旭，林波涛、陈文、丘水生，混沌神经网络的同步，华南理工大学学报(自然科学版)，1998，26(1-2):19-22.
[179] Ghobad Heidari-Bateni, and Clare D. McGllem. A chaos direct sequence spread-spectrum communication system. IEEE Trans. Commun. 1994, 42(2/3/4):1524-1527.
[180] Cuan Lian Koh and Toshimitisu Ushio. Digital communication method based on m-synchronized chaotic systems, IEEE Trans. CAS-1. 1997,44(5):383-390.
[181] Géza Kolumbán, Michael Peter Kennedy and Leon O. Chua. The role of synchronization in digital communications using chaos-part II: chaotic modulation and chaotic synchronization. IEEE Trans. CAS-1,1998,45(11):1129-1139.
[182] Gregory D. Vanwiggeren and Rajarshi Roy. Chaotic communication using time-delayed optical systems. Int. J. Bufurc. Chaos. 1999,9(11):2129-2156.
[183] 凌聪，孙松庚．Logistic映射跳频序列．电子学报，1997,25(10):79-81.
[184] Kari H. K?rkk?inen. Meaning of maximum and mean-square cross-correlation as a performance measure for CDMA code families and their influence on system capacity. IEICE Trans. Commun. 1993,E76-B(8):848-854.
[185] ?mer Morgül, Moez Feki, A chaotic masking scheme by using synchronized chaotic systems, Pysics Letter A 251(1999):169-176.
[186] 周红，凌燮亭，混沌保密通讯原理极其保密性分析，电路与系统学报，1996，1(3)：57-62.
[187] Giuseppe Grassi and Saverio Mascolo, Synchronizing Hyperchaotic system by observer design, IEEE TRANS. on CAS-Ⅱ,1999,46(4):478-483.
[188] 罗定军，张祥，董梅芳，动力系统的定性与分支理论，科学出版社，2001
[189] 盛昭翰，马军海. 非线性动力学系统分析引论. 科学出版社，2001.
[190] 陈式刚，映射与混沌，国防工业出版社，1992.
[191] 陆启韶，分岔与奇异性，上海科技教育出版社，1995.
[192] Hassard, B D. Theory and applications of Hopf bifurcation. Cambridge University Press 1981.
[193] K.Jack Hale, and Sjoerd M. Verduyn Lunel，Introduction to Functional Differential Equations, New York, Springer-verlag, Inc. , 1993.
[194] 刘昌伟. 关于李雅普诺夫指数的 Jacobi算法. JOURNAL OF WUHAN INSTITUTE OF CHEMICAL TECHNOLOGY, 1997, 19(4):82-85.
[195] 张家树，肖先赐. 混沌时间序列的Volterra自适应预测. 物理学报, 2000, 49(3):403-407.
[196] K.L.Babcock and R.M.Westervelt, Dynamics of simple electronic neural networks, Physical D,1987,28(3):305-316.
[197] M. G. Rosenblum, A. S. Pikovsky, J. Kurtbs. Phase Synchronization of Chaotic Oscillators. Phys. Rev. Lett., 1996,76:1804-1807.
[198] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J. Phase synchronization in driven and coupled chaotic oscillators. IEEE Transactions on CAS- I: Fundamental Theory and Applications, 44(10): 874 -881.
[199] Seon Hee Park , Seunghwan Kim, Hyeon-Bong Pyo et al. Effects of time-delayed interations on dynamic patterns in a coupled phase oscillater system. Phys. rev. 1999, 60(4):4962-4965.
[200] Seon Hee Park , Seunghwan Kim, Hyeon-Bong Pyo et al. Effects of time-delayed interations on dynamic patterns in a coupled phase oscillater system. Phys. rev. 1999, 60(4):4962-4965.
[201] Dabrowski A, Galias Z., Ogorzalek M.J. Phase synchronization phenomena in generalized CNN composed of chaotic cells.(CNNA 2000). Proceedings of the 2000 6th IEEE International Workshop on Cellular Neural Networks and Their Applications, 2000: 253 -258.
[202] K. Pyragas, Synchronization of coupled time-delay systems: Analytical estimations, Phy. Rev. E, 1998,58(3):3067-3071.
[203] Yu-Chu Tian, Furong Gao. "Adaptive control of chaotic continuous-time systems with delay". Physical D, 117(1998):1-12.
[204] Tao Yang, Chun-Mei Yang, Lin-Bao Yang. "A Detailed Study of Adaptive Control of Chaotic System with Unknown Parameters". Dynamics and Control. 1998, 8: 255-267.
[205] X. Yu. "Tracking inherent periodic orbits in chaotic systems via adaptive time delayed self-control". In Proc. IEEE int. Conf. Decision Control, San Diego, CA, 1997, l:401-405.
[2] Xiaofeng Liao, Kwok-Wo Wong, Zhongfu Wu, and Guanrong Chen. Novel Robust Stability Criteria for interval-Delayed Hopfield Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 2001, 48(11):1355-1359.
[3] 张锦炎，冯贝叶. 常微分方程几何理论与分支问题. 北京大学出版社，北京，2000年.
[4] Xiaofeng Liao, Zhongfu, and Juebang Yu, Hopf bifurcation analysis of a neural system with a continuously distributed delay, International Symposium on Signal Processing and Intelligent System, Guangzhou ,China ,Nov. 1999. P.546-549.
[5] Xiaofeng Liao, Zhongfu and Juebang Yu, Stability switches and bifurcation analysis of a neural network with continuously distributed delay, IEEE Trans. On SMC-I, 1999,29(6),692-696.
[6] K. Gopalsamy, I. Leung, Delay induced periodicity in a neural network of excitation and inhibition, Physica D, 89(1996),395-426.
[7] 廖晓峰，吴中福，虞厥邦，带分布时延神经网络：从稳定到振荡再到稳定的动力学现象，电子与信息学报， 2001, 23(7):689-692.
[8] Xiaofeng Liao, Kwok-wo Wong, Zhongfu Wu, Bifurcation analysis in a two-neuron system with continuously distributed delays. Physica D, 2001,179(1/2): 123-141.
[9] 靳 藩编著. 神经计算智能基础. 西南交通大学出版社, 成都, 2000年.
[10] K. Murali, M. Lakshmanan, and L. O. Chua. The Simplest Dissipative Nonautonomous Chaotic Circuit. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1994, 41(6):462-463.
[11] Hongtao Lu, Yongbao He, and Zhenya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1998, 45(2):178-181.
[12] Marco Gilli. Strange Attractors in Delayed Cellular Neural Networks. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1993, 40(11):849-853.
[13] Hongtao Lu and Zhenya He. Chaotic Behavior in First-Order Autonomous Continuous-Time Systems with Delay. IEEE Trans. on CAS-I: Fundamental Theory and Applications. 1996, 43(8):699-702.
[14] K. Gopalsamy and Issic K. C. Leung. Convergence under Dynamical Thresholds with Delay. IEEE Trans. on Neural Networks. 1997, 8(2):341-348.
[15] J. Belair, S. Dufour, Stability in a three-dimensional system of delay-differential equations, Can. Appl. Math. Quart. , 1996,4(2),135-156.
[16] L. Olien, J. Belair, Bifurcations, stability and monotonicity properties of a delayed neural network model", Physica D, 102(1997), 349-363.
[17] 周尚波，廖晓峰，虞厥邦. 具有任意激活函数的时延神经元方程的Hopf 分岔，电子科学学刊.
[18] Hongtao Lu and Zhengya He. Chaotic Behavior in first-order Autonomous Continuous-time systems with delay. IEEE trans. on CAS-1, 1996, .43(8):700-702.
[19] Xin Wang. Period-Doubling to Chaos in A Simple Neural Network. Neural Networks, IJCNN-91-Seattle International Joint Conference on, 1991, Vol.2, pp:333-339.
[20] Li XIE, Xing HE, Weidong ZHANG, Xiaoming XU. Single Chaotic Neuron with Time-Delay. Circuits and Systems, IEEE APCCAS 2000, the 2000 IEEE Asia-pacific Conference on, pp.809-812.
[21] Yu-Chu Tian and Furong Gao. Simple Delay Systems with Chaotic Dynamics. Control of Oscillations and Chaos, 1997, Proceedings, 1997 1st International Conference, Vol.2, pp.319-320.
[22] Hongtao Lu, Yongbao He, and Zhengya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks. IEEE trans. on CAS-1, 1996, 45(2):178-181.
[23] Givalleri P P.. Gilli M. and L. Pandolfi. On stability of cellular neural networks with delay. IEEE trans. on CAS, 1993, 40(3):157-165
[24] J. Cao. Global stability analysis in delayed cellular neural networks. Phys. Rev. E. 59(1999):5940-5944.
[25] S. Arik and V. Tavanoglu. On the global symptotic stability of delayed cellular neural networks. IEEE trans. on CAS-1, 47:571-574, 2000.
[26] J. Cao. Periodic solutions and exponential stability in delayed cellular neural networks. Phys. Rew. E, 60(1999):3244-3248.
[27] J. Cao.On stability of delayed cellular neural networks. Phys. Lett. A, 261(1999):303-308.
[28] T. Roska, C. W. Wu and L. O. Chua. Stability of cellular neural networks with dominant nonlinear and delay-type template, IEEE trans. on CAS-1, 1993, 40:270-272.
[29] T. Roska, C. W. Wu, M. Balsi and L. O. Chua. Stabilty and dynamics of delay-type general and cellular neural networks. IEEE trans. on CAS-1, 1992, 39:487-490.
[30] M. Gilli. Stability of cellular neural networks and delayed cellular neural networks with nonpostive template and nonmononic output functions. IEEE trans. on CAS-1, 1999, 41:518-528.
[31] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs. IEEE trans. on CAS-1, 45:168-171, 1998.
[32] S. Arik and V. Tavsanoglu. On the global asymptotic stability of delayed cellular neural networks. IEEE trans. on CAS-1, 2000, 47:571-574.
[33] Xiaofeng Liao, Kwok-Wo Wong, Juebang Yu. Novel Stability conditions for Cellular Neural Networks with Time Delay. International Journal of Bifurcation and Chaos. 2000, 11(7):1853-1864.
[34] Liaofeng Liao and Juebang Yu. Robust Stability for Interval Hopfield Neural Network with Time Delay. IEEE Trans. on Neural Network. 1998, 9(5):1042-1045.
[35] P. Celka. Chaotic Synchronization and Moduluation of Nonlinear Time-Feedback Optical Systems. IEEE Trans. on CAS-Ⅰ:Fundamental Theory and Applications, 1995,42(8):455-463.
[36] A.Londei, C.Mazio. A Controlled Chaotic Neural Network for Storing and Retriving Information. CNNA'96:Fourth IEEE international workshop Neural Network and their Applications. Sevitte, Spain, June 24-26, 1996, pp.51-56.
[37] Yang Biao, Kuang Jiaoxun. The PmL-stability of Implicit Runge-Kutta Methods for Delay Differential Equations. J. of Shanghai Teachers Univ.(Natural Science), 28(1):8-15, 1999.
[38] 丛玉豪，匡蛟勋. 数值求解时延微分的步长准则. 计算数学, 23(2):139-144, 2001
[39] 杨维明编著，时空混沌和耦合映象格子，上海科技教育出版社，上海，1994.
[40] 王炎，廖晓峰，吴中福，虞厥邦，一个带时延神经网络的分岔现象研究，电子科学学刊， 2000, 22(7):972-977.
[41] 周作领，符号动力系统，上海科技出版社，1997.
[42] Harold Szu,Richard Yentis C. Charies C. el. at.. Chaotic Neural Models and Artificial Networks. Proceedings of 1993 International Joint Conference on Neural Networks. Pp. 1473-1476.
[43] Kevin Judd and Kazuyuki Aihara. Neural Network and Chaos. 1992 IEEE International Symposium on Circuit and Systems, 6(1992):2765-2768.
[44] Yuyao He, Lipo Wang. Chaotic Neural Networks and Their Applications. Proceedings of 3rd World Congress on Intelligent Control and Automation. 2000, pp. 826-830.
[45] Zou F, Nossek J A. Bifurcation and chaos in cellular neural networks. IEEE Circuits and Systems. 1993, 40 (3):341-348.
[46] Andrew M.Fraser. Information and Entropy in Strange Attactors. IEEE Trans. on information theory. 1989, 35(2):245-262.
[47] D.Ruelle. Ergodic Theory of chaos and strange attractors. Rew. Mod. Phys. 1985, 57(3-4): 617-1115
[48] Ippei Shimada and Tomomasa Nagashima. A Numerical Approach to Erogodic Problem of Dissipative Dynamical Systems. Progress of Theoretical Physics, 1979, 61(6): 1605-1616
[49] Thomas S. Parker, Leon O. Chua. Practical Numerical Algorithms for Chaotic Systems. Springer_Verlag, World Publishing Corp. 1992.
[50] Yuquan He, Ruidong Chi and Naiwen He. Lyapunov exponents of the circle map in human hearts. Phys. Lett. A, 170(1992):29-32.
[51] X. Zeng, R. Eykholt, and R. A. Pielke. Estimating the Lyapunov-Exponent Spectrum from Short Time Series of Low Precision. Phys. Rev. Lett. 1991,66(25):3229-3232.
Di He, Cheb He, Ling-go Jiang, Hong-wen Zhu, and Guang-rui Hu. Chaotic Characteristic of a One-Dimensional Iterative Map with Infinite Collapses. IEEE Trans. on CAS-I:
[52] Fundamental Theory and Applications, 2001, 48(7):900-906.
[53] 马军海, 陈予恕,刘曾荣, 动力系统实测数据的Lyapunov指数的矩阵算法, 应用数学与力学, 1999，20(9):919-927.
[54] 杨绍清. 一种最大李雅普诺夫指数估计的稳健算法, 物理学报, 2000, 49(04):636-640.
[55] Yan Hong Lim, David C. Hamill. Problem of Computing Lyapunov Exponents In Power Electronics. Circuits and Systems, ISCAS'99, 1999, 5(5):297-301.
[56] Holger Kantz. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A, 185(1994):77-87.
[57] Keith Briggs. An improved method for estimating Liapunov exponents of chaotic time series. Phys. Lett. A, 1990,151(1,2):27-32.
[58] 陈关荣. 控制动力学系统的分岔现象. 控制理论与应用, 2001, 18(2):153-159
[59] Xiao Fan Wang, Guanrong Chen. Controlling bifurcating dynamics via chaotification. Decision and Control, Proceedings of the 40th IEEE Conf. on , 2001, 1: 692 -697.
[60] Sang-Ho Lee. Jong-Keun Park, Byung-Ha Lee. A study on the nonlinear controller to prevent unstable Hopf bifurcation. Power Engineering Society Summer Meeting, 2001 ,2: 978 -982.
[61] Wang Y. Bifurcation control in systems governed by functional differential equations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 5: 4409 -4414.
[62] Alonso, D.; Paolini, E.; Moiola, J. On anticontrol of Hopf bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3 : 2072 -2077.
[63] MingQing Xiao, Wei Kang. Feedback control of Hopf bifurcations via integral averaging method. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3: 2066 -2071.
[64] Guanrong Chen, Yap, K.C. Jialiang Lu Feedback control of Hopf bifurcations. Circuits and Systems, SCAS '98. Proceedings of the 1998 IEEE International Symposium on ,3: 639 -642.
[65] Wang, Y. Murray R.M. Feedback stabilization of steady-state and Hopf bifurcations. Decision and Control, Proceedings of the 37th IEEE Conf. on , 1998, 3: 2431 -2437.
[66] Moiola, J.L., Berns, D.W., Guanrong Chen Feedback control of limit cycle amplitudes. Decision and Control, Proceedings of the 36th IEEE Conf. on , 1997, 2: 1479 -1485.
[67] Nakajima, H., Ueda Y. On the stability of delayed feedback control of chaos. Control of Oscillations and Chaos, Proceedings., 1st International Conf. , 1997, 3: 411 -414.
[68] Moiola, J.L., Chen G. Hopf bifurcations in time-delayed nonlinear feedback control systems. Decision and Control, Proceedings of the 34th IEEE Conf. on , 1995, 1: 942 -948.
[69] Genesio, R., Tesi A., Wang H.O., Abed E.H. Control of period doubling bifurcations using harmonic balance. Decision and Control, Proceedings of the 32nd IEEE Conf. on , 1993. 1: 492 -497.
[70] Colonius F., Hackl G., Kliemann W. Controllability near a Hopf bifurcation. Decision and Control, Proceedings of the 31st IEEE Conf. on , 1992, 2: 2113 -2118.
[71] Nakajima H. Ueda Y. On the stability of delayed feedback control of chaos. Control of Oscillations and Chaos, Proceedings., 1st International Conf. , 1997, 3: 411 -414.
[72] Moiola J.L., Chen G. Hopf bifurcations in time-delayed nonlinear feedback control systems. Decision and Control, Proceedings of the 34th IEEE Conf. on , 1995, 1:942 -948 .
[73] Alonso D., Paolini E., Moiola J. On anticontrol of Hopf bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 3: 2072 -2077.
[74] MingQing Xiao, Wei Kang. Feedback control of Hopf bifurcations via integral averaging method. Decision and Control, Proceedings of the 39th IEEE Conf. on, 2000, 3: 2066 -2071.
[75] Juan Li, Venkatasubramanian V. Study of Hopf bifurcations in a simple power system model. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 4: 3075 -3079.
[76] Hamzi B., Kang W., Barbot J.-P. On the control of Hopf bifurcations.Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 2: 1631 -1636.
[77] Hua O. Wang, Dong S. Chen, Bushnell L.G. Dynamic feedback control of bifurcations. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000, 2: 1619 -1624.
[78] Chang D.-E., Kang W., Krener A.J. Normal forms and bifurcations of control systems. Decision and Control, Proceedings of the 39th IEEE Conf. on , 2000 , 2: 1602 -1607.
[79] D'Amico, M.B., Moiola, J.L., Paolini E.E. Hopf bifurcation in discrete-time systems via a frequency domain approach. Control of Oscillations and Chaos, 2000. Proceedings. 2nd International Conf. , 2000, 2: 290 -293.
[80] Tomashevskiy, A.I.; Kapranov, M.V. Bifurcations and chaos in amplifier phase control systems. Control of Oscillations and Chaos, Proceedings. 2nd International Conf. , 2000, 3: 530 -535 .
[81] 刘向东. Hopf分岔方向控制的频域方法. 非线性动力学学报, 1998, 5(1):69-74.
[82] Dong Chen; Wang H.O.; Guanrong. Chen Anti-control of Hopf bifurcations through washout filters. Decision and Control, Proceedings of the 37th IEEE Conf. on , 1998, 3: 3040 -3045.
[83] Lerm, A.A.P. Control of hopf bifurcation in power systems via a generation redispatch. Power Tech Proceedings, IEEE Porto , 2001,2: 6-10.
[84] 方锦清. 非线性系统中混沌的控制与同步及其应用前景(一)[J]. 物理学进展，1996，16(1):1-7.
[85] 方锦清. 非线性系统中混沌的控制方法、同步原理及其应用前景(二)[J]. 物理学进展，1996，16(2):137-202.
[86] Pecora M., Carroll L. Synchronization in Chaotic System. Phys. Rev. Lett., 1990, 65(8):821-823.
[87] Pecora M., Carroll L. Driving System with Chaotic System. Phys. Rev. Lett., 1991, 44(4):2374-2383.
[88] Macief. Oyorzalek, Taming Chaos: Part II ? Control, IEEE Trans. Circuits syst.-1, 1993， 40(10) :693-699.
[89] 禹思敏, 丘水生. 混沌系统及混沌神经网络同步的研究. 广东工业大学学报, 2000, 17(4):1-5.
[90] Shinbrot T., Grbogi C., Ott E., Yorke J. A., Using small perturbations to control chaos[J], Nature, 1993, 363:411-417.
[91] Tetsuro Eudo and Leo O. Chua. Synchronization of Chaos in Phase-Locked Loops. IEEE Trans. on CAS. 1991, 38(12): 1580-1588.
[92] Edgar N. Sanchez, Jose P. Perez, Luis J. Ricalde et al. Chaos Synchronization Via Adaptive Recurrent Neural Control. Proceedings of the 40th IEEE Conference on Decision and Control 2001,ThP07-3:3536-3539.
[93] 李兵, 蒋蔚孙. 混沌优化方法及其应用. 控制理论与应用, 1997, 14(4): 613-615.
[94] 王光瑞，于熙龄，陈式刚编著，混沌的控制、同步与利用，国防工业出版社，2001.
[95] Edward Ott, Celso Drebogi, and James A. Yorke. Controlling Chaos. Phys. Rev. Lett. 1990, 64(11): 1196-1199.
[96] Yueming Zeng, Sahjendra N. Singh. Adaptive Control of Chaos in Lorenz System. Dynamics and Control. 7(1997):143-154.
[97] Guangrong Chen. Chaos: Control and Anti-Control. IEEE Circuits and Systems. 1998, 9 (1):3-6.
[98] Nigel Grook and Tjeerd Olde Scheper. An adaptive Chaotic Neural Network. Proceedings of the 2002 International Joint Conference, 2002, Vol.3, pp.2580-2585.
[99] A. Yu, Markov, A. L. Fradkov, G. S. Simin. Adaptive Synchronization of Chaotic Generators Based on Tunnel Diodes. Proceedings of the 35th Conference on Decision and Control. Kobe, Japan., December 1996.
[100] 钟国群，蔡氏电路混沌同步保密通讯，电路与系统学报，1996，1（1）
[101] 周尚波, 何松柏,虞厥邦,廖晓峰.用于保密通信的混沌跳频序列. 信号处理,2001,17(增刊):9-12.
[102] 何松柏,周尚波.一种用于混沌通信的跳频合成器设计.系统工程与电子技术，2002,24(3):11-13.
[103] 何松柏,王琪贤,周尚波.混沌无线通信研究. 信号处理, 2001,17(增刊):5-6.
[104] Veliko Milanovic and Mona E. Zaghloul. Synchronization of Chaotic Neural Networks for Secure Communictions.
[105] L.Kocarev, K.S.Halle and L.O.Chua. Experimental Demonstration of secure Communication via Chaotic Synchronization. Int. J. of Bifurcation and Chaos. 2(1992):709-713.
[106] Y.Horio and K.Suyama. Experimental Verification of Signal Transmission Using Synchronized SC Chaotic Neural Networks. IEEE Tran. CAS I, 1995,42(7):393-395.
[107] 李忠，毛宗源，混沌控制综述，电路与系统学报，1998，3（1）：59-65.
陈德钊，董军，胡上序，混沌动力学在智能信息处理中的应用研究现状，计算机科学，
[108] Vol.25, No.3 1998
[109] Kazuo Tanaka, Takayuki Ikeda, and Hua O. Wang, A unified Approach to controlling Chaos via an LMI-Based Fuzzy Control System Design, IEEE Trans. Circuits Syst.-1, 1998, 45(10):
[110] 夏承铨，三阶非自治电路中的混沌振荡，电路与系统学报，Vol.1, No.2, 1996
[111] Yao Y, Freeman W. J.Model of biological pattern recognition with spatially dynamics. Neural Networks, 1990,3:153-170.
[112] 陆燕，杜继宏，李春文，延时时间未知的时延系统神经网络补偿控制，清华大学学报(自然科学版)，1998，38(9):67-69.
[113] Sitte R.,Sitte J. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series. IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2000,30(4): 568 -572.
[114] Ming-Hsuan Yang, Ahuja N., Tabb M..Extraction of 2D motion trajectories and its application to hand gesture recognition., IEEE Trans. on Pattern Analysis and Machine Intelligence. 2002, 24(8) :1061 -1074.
[115] Hirasawa K, Murata J, Jinglu Hu, Chunzhi Jin. Universal learning network and its application to robust control. IEEE Trans. on Systems, Man and Cybernetics, Part B, 2000，30(3): 419 -430.
[116] Li Xinhong, Wang Shaobo. Adaptive PIP controller based on neural network for time-delay systems and its applications. Int. Conf. on Info-tech and Info-net Proceedings. 4(2001 ):346 -351.
[117] Woods, W.P.; Johnson, S.R. Comparison of the response of a time delay neural network with an analytic model. Proceedings of the 2002 Int. Joint Conf. on Neural Networks, 2002, vol.2, pp.1120-1125.
[118] Sitte R, Sitte J.. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series ., IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews , 2000, 30(4 ):568 -572.
[119] Sick B. Online tool wear monitoring in turning using time-delay neural networks. Proceedings of the 1998 IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 1998, Volume: 1 .pp:445 -448.
[120] Ning Lan, Hua-Quan Feng, Crago P.E. Neural network generation of muscle stimulation patterns for control of arm movements. IEEE Trans. on Neural Systems and Rehabilitation Engineering, 1994,2(4):213 -224.
[121] Wang X. Text-Dependent speaker verification using recurrent time delay neural networks for feature extraction . Neural Networks for Processing [1993] III. Proceedings of the 1993 IEEE-SP Workshop , 1993, pp:353 -361.
[122] Fang Y.H., Yagoub M.C.E., Wang F., Zhang Q.J. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks. Microwave Symposium Digest. 2000 IEEE MTT-S International, Volume: 2, pp. 883 -886.
[123] Yonghua Fang, Yagoub M.C.E.,Fang Wang, Qi-Jun Zhang. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks., IEEE Transactions on Microwave Theory and Techniques, 48(12): 2335 -2344.
[124] Nakagawa S., Hirata Y. Comparison among time-delay neural networks, LVQ2 discrete parameter HMM and continuous parameter HMM. 1990, vol.1, pp.509 -512.
[125] Waibel A., Hanazawa T., Hinton G., Shikano K., Lang K. Phoneme recognition: neural networks vs. hidden Markov models vs. hidden Markov models. Int. Conf. on Acoustics, Speech, and Signal Processing, 1988, vol.1, pp.107 -110.
[126] Dugast C., Devillers L. Incorporating acoustic-phonetic knowledge in hybrid TDNN/HMM frameworks. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992, Volume: 1, pp.421 -424.
[127] Oweiss K., Abdel Alim O. Performance evaluation of time-delay fuzzy neural networks for isolated word recognition. Int. Symposium on Neuro-Fuzzy Systems, 1996, pp.203 -211.
[128] Mastorocostas P., Theocharis J.B. A generalized TSK dynamic fuzzy neural network: application to adaptive noise cancellation. The Ninth IEEE International Conference on Fuzzy Systems, 2000,Volume:2, pp.877 -882.
[129] Tan C.X., Tachibana H..Nonlinearity-tolerated active noise control using an artificial neural network. IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics, 1997,vol.4,pp.19-22.
[130] Thyssen J., Nielsen H., Hansen S.D. Non-linear short-term prediction in speech coding. 1994. ICASSP-94., 1:185 -188.
[131] Sitte R., Sitte J. Analysis of the predictive ability of time delay neural networks applied to the S&P; 500 time series. IEEE Trans. on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2000, 30(4):568 -572.
[132] Yu D.L., Williams D., Gomm J.B. On-line implementation of a model predictive controller on a multivariable chemical process. Model Predictive Control: Techniques and Applications - Day 2 (Ref. No. 1999/096), IEE Two-Day Workshop on , 1999, 2:1 -5.
[133] Gatt, E., Micallef, J., Micallef, P., Chilton, E. Phoneme classification in hardware implemented neural networks., The 8th IEEE Int. Conf. on Electronics, Circuits and Systems, 2001, Volume: 1, pp.481 -484.
[134] Jedra, M., El Khattabi, N., Limouri, M., Essaid A. Recognition of seed varieties using neural networks analysis of electrophoretic images., Proceedings of the IEEE-INNS-ENNS Int. Joint Conf. on Neural Networks, 2000, Volume: 5, pp.521 -526.
[135] Gatt, E., Micallef, J., Chilton, E. An analog VLSI time-delay neural network implementation for phoneme recognition. Proceedings of the 2000 6th IEEE Int. Workshop on Cellular Neural Networks and Their Applications, 2000 ,pp.315 -320.
Jiang Minghu, Yuan Baozong, Tang Xiaofang, Lin Biqin. Fast learning algorithms for time-delay neural networks phoneme recognition. The Fourth Int. Conf. on Signal
[136] Processing Proceedings, 1998 , vol.1. pp.730 -733 .
[137] Selouani S.-A., Caelen, J. Arabic phonetic features recognition using modular connectionist architectures. IEEE 4th Workshop on Interactive Voice Technology for Telecommunications Applications, 1998. Proceedings. Pp.155 -160.
[138] Hui W.M., Liu P.C.K., Li K.C. Cantonese phonemes recognition using modular neural network approach. IEEE Int. Symposium on Information Theory Proceedings, 1997, pp. 210.
[139] Islam, R., Hiroshige, M., Miyanaga, Y., Tochinai, K. Phoneme recognition using modified TDNN and a self-organizing clustering network. IEEE Int. Symposium on Circuits and Systems, 1995 , Volume: 3, pp.1816 -1819.
[140] Duanpei Wu, Gowdy J.N. Tunable time delay neural networks for isolated word recognition. Southeastcon '95. Visualize the Future., Proceedings., IEEE , 1995 ,pp.220 -223.
[141] Dugast C., Devillers L., Aubert, X. Combining TDNN and HMM in a hybrid system for improved continuous-speech recognition. IEEE Trans. on Speech and Audio Processing, 1994, Part: 2 , 2(1):217 -223.
[142] Minh Tue Vo. Incremental learning using the time delay neural network. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 1994, II: 629 -632.
[143] Berthold M.R. A time delay radial basis function network for phoneme recognition. Neural Networks, 1994. IEEE World Congress on Computational Intelligence., 1994 IEEE Int. Conf. on , 1994, 7: 4470 -4472.
[144] Weber, D.M. Parallel implementation of time delay neural networks for phoneme recognition. EEE International Conference on Neural Networks, 1993, vol.3, pp.1583 -1587.
[145] Jang C.S., Un C.K. Integrating time-delay neural networks and fuzzy HMM for phoneme-based word recognition. Electronics Letters, 1992, 28(25):2319 -2320.
[146] Wendell T.C., Abdelhamied K. A phoneme recognition system using modular construction of time-delay neural networks. Proceedings., Fifth Annual IEEE Symposium on Computer-Based Medical Systems, 1992, pp.704 -709.
[147] Takami J., Kai A., Sagayama S. Speech recognition by combining pair wise discriminant time-delay neural networks and predictive LR-parser. Neural Networks for Signal Processing, Proceedings of the 1991 IEEE Workshop, pp.327 -336.
[148] Sugiyama M., Sawai H., Waibel A.H. Review of TDNN (time delay neural network) architectures for speech recognition. IEEE Int. Symposium on Circuits and Systems, 1991, vol.1, pp.582 -585.
[149] Bennani Y., Chaourar N., Gallinari P., Mellouk A. Validation of neural net architectures on speech recognition tasks. Int. Conf. on Acoustics, Speech, and Signal Processing, vol.1, pp. 97 -100.
Bimbot F., Chollet G., Tubach, J.-P. TDNNs for phonetic features extraction: a visual
[150] exploration, Int. Conf. on Acoustics, Speech, and Signal Processing, 1991, vol.1,pp.73 -76.
[151] Sawai H. TDNN-LR continuous speech recognition system using adaptive incremental TDNN training, International Conference on Acoustics, Speech, and Signal Processing, 1991, vol.1, pp. 53 -56
[152] Sawai H. Frequency-time-shift-invariant time-delay neural networks for robust continuous speech recognition. 1991, vol.1, pp. 45 -48.
[153] Hampshire J.B. Waibel A.H. A novel objective function for improved phoneme recognition using time-delay neural networks. IEEE Trans. on Neural Networks, 1990, 1(2):216 -228.
[154] Kiseok Kim, Inbum Kim, Heeyeung Hwang. A study on the recognition of the Korean monothongs using artificial neural net models. Information Technology, 1990. 'Next Decade in Information Technology', Proceedings of the 5th Jerusalem Conference on (Cat. No.90TH0326-9) , 1990, pp.364 -371.
[155] Shaw A., Mitchell R.A. Phoneme recognition with a time-delay neural network. Neural Networks, 1990., 1990 IJCNN Int. Joint Conf. on , 1990, vol.2, pp.191 -195.
[156] Ma W., Van Compernolle D. TDNN labeling for a HMM recognizer. Acoustics, Speech, and Signal Processing, 1990 Int. Conf. on , 1990, vol.1, pp.421 -423.
[157] Hampshire J.B., Waibel A.H. The Meta-Pi network: connectionist rapid adaptation for high-performance multi-speaker phoneme recognition. Int. Conf. on Acoustics, Speech, and Signal Processing , 1990, vol.1, pp.165 -168.
[158] Hampshire J.B., Waibel A.H. A n_ovel objective function for improved phoneme recognition using time delay neural networks. Int. Joint Conf. on , 1989, vol.1, pp. 235 -241.
[159] Waibel A, Sawai H., Shikano K. Consonant recognition by modular construction of large phonemic time-delay neural networks. Int. Conf. on Acoustics, Speech, and Signal Processing, 1989, vol.1, pp.112 -115.
[160] Rivlin Z. Telephones you can talk to. IEEE Potentials , 1989, 8(4): 13 -16.
[161] Waibel A., Hanazawa T., Hinton G., Shikano K., Lang K.J. Phoneme recognition using time-delay neural networks. IEEE Trans. on Acoustics, Speech and Signal Processing, 37(3): 328 -339.
[162] Jiang Minghu, Zhu Xiaoyan. A novel fast learning algorithms for time-delay neural networks.Int. Joint Conf. on Neural Networks, 1999, Volume: 2, pp.1380 -1383.
[163] Sawai H., Waibel A., Miyatake M., Shikano K. Spotting Japanese CV-syllables and phonemes using the time-delay neural networks. Int. Conf. on Acoustics, Speech, and Signal Processing, 1989. vol.1, pp.25 -28 .
[164] Sawai H., Waibei A., Haffner P. et al. Parallelism, hierarchy, scaling in time-delay neural networks for spotting Japanese phonemes CV-syllables., Int. Joint Conf. on Neural Networks, 1989, vol.2, pp.81 -88.
[165] Miyatake M., Sawai H., Minami Y., Shikano K. Integrated training for spotting Japanese phonemes using large phonemic time-delay neural networks. Acoustics, Speech, and Signal Processing, Int. Conf. on , 1990, vol.1, pp. 449 -452.
[166] Lavagetto F. Time-delay neural networks for estimating lip movements from speech analysis: a useful tool in audio-video synchronization. IEEE Trans. on Circuits and Systems for Video Technology, 1997 , 7(5): 786 -800.
[167] Lavagetto F, Lepsoy S, Braccini C, Curinga S. Lip motion modeling and speech driven estimation. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 1997 , Volume: 1 , pp.183 -186.
[168] Kiseok Kim, Inbum Kim, Heeyeung Hwang. A study on the recognition of the Korean monothongs using artificial neural net models. Information Technology, 1990. 'Next Decade in Information Technology', Proceedings of the 5th Jerusalem Conf. on (Cat. No.90TH0326-9) , 1990,pp.364 -371.
[169] Coggins K.M., Pricipe J. Detection and classification of insect sounds in a grain silo using a neural network. Proceedings of IEEE Int. Joint Conf. on Neural Networks,1998 , Volume: 3 , pp.1760 -1765.
[170] 钟林,刘润生 . 新神经网络结构及其在数码语音识别中的应用. 清华大学学报(自然科学版)，2000，40（3）:27-32.
[171] Mingyu Li, Shangbo Zhou , Songbai He, Juebang Yu Radial Basis Function Neural Networks Models for Power-Amplifier Design, to be submitted.
[172] Y onghua Fang, Yagoub, M.C.E, Fang Wang, and Qi-Jun Zhang. A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks", IEEE Trans. Microwave theory Tech, 2000, 48(12):2335-2344.
[173] 肖怀铁,付强,庄钊文等,宽带毫米波雷达目标时延神经网络识别新方法. 红外与毫米波学报，2001，20（6）：459-463.
[174] Shi K.L. et Al., Direct self control of induction motor based on neural network. Industry Applications, IEEE Trans. on , 2001, 37(5):1290 -1298.
[175] Kurita Y., Hashimoto T., Ishida Y. An application of time delay estimation by ANNs to frequency domain adaptive I-PD controller. Int. Joint Conf. On Neural Networks, 1999, Volume: 3 , pp.2164 -2167.
[176] Balestrino A., Verona F.B., Landi A. Online process estimation by ANNs and Smith controller design. Control Theory and Applications, IEE Proceedings- , 1998, 145 (2): 231 -235.
[177] Zhang Shu-Ling, Xie Ke-ming. The intelligent learning control using single neuron and its application in an industrial boiler. IEEE Int. Conf. on Intelligent Processing Systems. 1997, Volume: 1 , pp. 797 -800.
[178] 钟晓旭，林波涛、陈文、丘水生，混沌神经网络的同步，华南理工大学学报(自然科学版)，1998，26(1-2):19-22.
[179] Ghobad Heidari-Bateni, and Clare D. McGllem. A chaos direct sequence spread-spectrum communication system. IEEE Trans. Commun. 1994, 42(2/3/4):1524-1527.
[180] Cuan Lian Koh and Toshimitisu Ushio. Digital communication method based on m-synchronized chaotic systems, IEEE Trans. CAS-1. 1997,44(5):383-390.
[181] Géza Kolumbán, Michael Peter Kennedy and Leon O. Chua. The role of synchronization in digital communications using chaos-part II: chaotic modulation and chaotic synchronization. IEEE Trans. CAS-1,1998,45(11):1129-1139.
[182] Gregory D. Vanwiggeren and Rajarshi Roy. Chaotic communication using time-delayed optical systems. Int. J. Bufurc. Chaos. 1999,9(11):2129-2156.
[183] 凌聪，孙松庚．Logistic映射跳频序列．电子学报，1997,25(10):79-81.
[184] Kari H. K?rkk?inen. Meaning of maximum and mean-square cross-correlation as a performance measure for CDMA code families and their influence on system capacity. IEICE Trans. Commun. 1993,E76-B(8):848-854.
[185] ?mer Morgül, Moez Feki, A chaotic masking scheme by using synchronized chaotic systems, Pysics Letter A 251(1999):169-176.
[186] 周红，凌燮亭，混沌保密通讯原理极其保密性分析，电路与系统学报，1996，1(3)：57-62.
[187] Giuseppe Grassi and Saverio Mascolo, Synchronizing Hyperchaotic system by observer design, IEEE TRANS. on CAS-Ⅱ,1999,46(4):478-483.
[188] 罗定军，张祥，董梅芳，动力系统的定性与分支理论，科学出版社，2001
[189] 盛昭翰，马军海. 非线性动力学系统分析引论. 科学出版社，2001.
[190] 陈式刚，映射与混沌，国防工业出版社，1992.
[191] 陆启韶，分岔与奇异性，上海科技教育出版社，1995.
[192] Hassard, B D. Theory and applications of Hopf bifurcation. Cambridge University Press 1981.
[193] K.Jack Hale, and Sjoerd M. Verduyn Lunel，Introduction to Functional Differential Equations, New York, Springer-verlag, Inc. , 1993.
[194] 刘昌伟. 关于李雅普诺夫指数的 Jacobi算法. JOURNAL OF WUHAN INSTITUTE OF CHEMICAL TECHNOLOGY, 1997, 19(4):82-85.
[195] 张家树，肖先赐. 混沌时间序列的Volterra自适应预测. 物理学报, 2000, 49(3):403-407.
[196] K.L.Babcock and R.M.Westervelt, Dynamics of simple electronic neural networks, Physical D,1987,28(3):305-316.
[197] M. G. Rosenblum, A. S. Pikovsky, J. Kurtbs. Phase Synchronization of Chaotic Oscillators. Phys. Rev. Lett., 1996,76:1804-1807.
[198] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J. Phase synchronization in driven and coupled chaotic oscillators. IEEE Transactions on CAS- I: Fundamental Theory and Applications, 44(10): 874 -881.
[199] Seon Hee Park , Seunghwan Kim, Hyeon-Bong Pyo et al. Effects of time-delayed interations on dynamic patterns in a coupled phase oscillater system. Phys. rev. 1999, 60(4):4962-4965.
[200] Seon Hee Park , Seunghwan Kim, Hyeon-Bong Pyo et al. Effects of time-delayed interations on dynamic patterns in a coupled phase oscillater system. Phys. rev. 1999, 60(4):4962-4965.
[201] Dabrowski A, Galias Z., Ogorzalek M.J. Phase synchronization phenomena in generalized CNN composed of chaotic cells.(CNNA 2000). Proceedings of the 2000 6th IEEE International Workshop on Cellular Neural Networks and Their Applications, 2000: 253 -258.
[202] K. Pyragas, Synchronization of coupled time-delay systems: Analytical estimations, Phy. Rev. E, 1998,58(3):3067-3071.
[203] Yu-Chu Tian, Furong Gao. "Adaptive control of chaotic continuous-time systems with delay". Physical D, 117(1998):1-12.
[204] Tao Yang, Chun-Mei Yang, Lin-Bao Yang. "A Detailed Study of Adaptive Control of Chaotic System with Unknown Parameters". Dynamics and Control. 1998, 8: 255-267.
[205] X. Yu. "Tracking inherent periodic orbits in chaotic systems via adaptive time delayed self-control". In Proc. IEEE int. Conf. Decision Control, San Diego, CA, 1997, l:401-405.