Lü系统的全局指数吸引集和正向不变集估计
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摘要
作为一个著名的混沌系统,Lü系统吸引集的精确估计具有重要的理论意义和实际应用。文章利用Lyapunov函数理论,给出了该系统的全局指数吸引集和正向不变集的估计。具体来说,就是将状态空间分成若干区域,在每一个区域上构造恰当的广义正定函数,结合经典技巧获得该估计;最后,通过仿真验证了估计的有效性。
As a famous chaotic system,accurate estimations for attractive set of Lü system has important theoretical significance and practical applications.In this paper,an estimation on globally exponentially attractive set and positive invariant set of Lüsystem is given by constructing several generalized positive Lyapunov functions.Specifically,the state space can be divided into several regions,and for each region an appropriate generalized positive definite function is constructed and the estimate is obtained by combining with classical technique.Finally,the validity of the estimates is shown through the simulation.
As a famous chaotic system,accurate estimations for attractive set of Lü system has important theoretical significance and practical applications.In this paper,an estimation on globally exponentially attractive set and positive invariant set of Lüsystem is given by constructing several generalized positive Lyapunov functions.Specifically,the state space can be divided into several regions,and for each region an appropriate generalized positive definite function is constructed and the estimate is obtained by combining with classical technique.Finally,the validity of the estimates is shown through the simulation.
引文
[1]CHEN G R,UTEA T.Yet another chaotic attractor[J].International Journal of Bifurcation and Chaos,1999,9(7):1465-1466.
[2]LV J H,CHEN G R.A new chaotic attractor coined[J].International Journal of Bifurcation and Chaos,2002,12(3):659-661.
[3]LV J H,CHEN G R,ZHANG S C.Dynamical analysis of a new chaotic attractor[J].International Journal of Bifurcation and Chaos,2002,12(5):1001-1015.
[4]DANCA M F.Synthesizing the Lüattractor by parameterswitching[J].International Journal of Bifurcation and Chaos,2011,21(1):323-331.
[5]CHEN A M,LU J A,LV J H,et al.Generating hyperchaotic Lüattractor via state feedback control[J].Physica A,2006,364:103-110.
[6]SUDHEER K S,SABIR M.Hybrid synchronization of hyperchaotic Lu system[J].Indian Academy of Sciences,2009,73(4):781-786.
[7]RATCHAGIT K,PHAT V N.Stability of Lu’s system[C]//.2010 2nd International Conference on Computer Engineering and Technology.[S.l.]:IEEE,2010:648-651.
[8]廖晓昕,罗海庚,傅予力,等.论Lorenz系统族的全局指数吸引集和正向不变集[J].中国科学E辑:信息科学,2007,37(6):757-769.
[9]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001:41-46.
[10]廖晓昕,徐炳吉,陈关荣,等.Chen混沌系统全局指数吸引集和正向不变集的构造性证明及应用[J].中国科学E辑:信息科学,2015,45(1):129-144.
[11]ZHANG F C,MU C L,LI X W.On the boundness of some solutions of the Lüsystem[J].International Journal of Bifurcation and Chaos,2012,22(1):1250015-1-1250015-5.
[2]LV J H,CHEN G R.A new chaotic attractor coined[J].International Journal of Bifurcation and Chaos,2002,12(3):659-661.
[3]LV J H,CHEN G R,ZHANG S C.Dynamical analysis of a new chaotic attractor[J].International Journal of Bifurcation and Chaos,2002,12(5):1001-1015.
[4]DANCA M F.Synthesizing the Lüattractor by parameterswitching[J].International Journal of Bifurcation and Chaos,2011,21(1):323-331.
[5]CHEN A M,LU J A,LV J H,et al.Generating hyperchaotic Lüattractor via state feedback control[J].Physica A,2006,364:103-110.
[6]SUDHEER K S,SABIR M.Hybrid synchronization of hyperchaotic Lu system[J].Indian Academy of Sciences,2009,73(4):781-786.
[7]RATCHAGIT K,PHAT V N.Stability of Lu’s system[C]//.2010 2nd International Conference on Computer Engineering and Technology.[S.l.]:IEEE,2010:648-651.
[8]廖晓昕,罗海庚,傅予力,等.论Lorenz系统族的全局指数吸引集和正向不变集[J].中国科学E辑:信息科学,2007,37(6):757-769.
[9]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001:41-46.
[10]廖晓昕,徐炳吉,陈关荣,等.Chen混沌系统全局指数吸引集和正向不变集的构造性证明及应用[J].中国科学E辑:信息科学,2015,45(1):129-144.
[11]ZHANG F C,MU C L,LI X W.On the boundness of some solutions of the Lüsystem[J].International Journal of Bifurcation and Chaos,2012,22(1):1250015-1-1250015-5.