Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters

This Letter investigates the problem of synchronization between two different chaotic systems. A generic adaptive synchronization scheme is proposed for a class of chaotic systems with uncertain parameters. Based on the Lyapunov stability theorem, an adaptive controller and the corresponding parameters update laws are designed to synchronize two chaotic systems. Numerical simulations are also given to show the effectiveness of the proposed method.

[1]  Mark Hess,et al.  TRANSITION TO PHASE SYNCHRONIZATION OF CHAOS , 1998 .

[2]  Shaoqing Wang,et al.  An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems , 2002 .

[3]  Guanrong Chen,et al.  Synchronization stability of three chaotic systems with linear coupling , 2002 .

[4]  H. Agiza,et al.  Synchronization of Rossler and Chen chaotic dynamical systems using active control , 2001, Physics Letters A.

[5]  Jinhu Lu,et al.  Parameters identification and synchronization of chaotic systems based upon adaptive control , 2002 .

[6]  Peter Liu,et al.  Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[7]  Jinde Cao,et al.  Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification , 2007 .

[8]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[9]  Jamal Daafouz,et al.  Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification , 2005 .

[10]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[11]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[12]  Chun-Mei Yang,et al.  Impulsive control of Lorenz system , 1997 .

[13]  Tianping Chen,et al.  Robust synchronization of delayed neural networks based on adaptive control and parameters identification , 2006 .

[14]  Jinde Cao,et al.  Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. , 2005, Chaos.

[15]  Rongwei Guo,et al.  Identifying parameter by identical synchronization between different systems. , 2004, Chaos.

[16]  Shihua Chen,et al.  Synchronizing strict-feedback chaotic system via a scalar driving signal. , 2004, Chaos.

[17]  Zhongjun Ma,et al.  Generalized synchronization of different dimensional chaotic dynamical systems , 2007 .

[18]  E. M. Shahverdiev,et al.  Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback. , 2001, Physical review letters.

[19]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[20]  Jiang-Wen Xiao,et al.  Impulsive control for synchronization of a class of continuous systems. , 2004, Chaos.

[21]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Tianping Chen,et al.  Adaptive Synchronization of Coupled Chaotic Delayed Systems Based on Parameter Identification and its Applications , 2006, Int. J. Bifurc. Chaos.