Generalized Synchronization of Bidirectionally Coupled Chaotic Systems Via Linear Transformations

Several important properties of chaos synchronization of bidirectionally coupled systems remain still unexplored. This paper designes a new synchronization scheme for generalized bidirectionally coupled chaotic systems via linear transformations. The proposed synchronization scheme of bidirectionally coupled chaotic systems are discussed taking coupled unified chaotic systems. In this method, we can predict the driven systems behavior in advance, knowing the driving systems behavior. Simulation results are presented to show the effectiveness of the proposed scheme.

[1]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[2]  C. Chee,et al.  A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions , 2004 .

[3]  Swarup Poria The linear generalized chaos synchronization and predictability , 2007 .

[4]  Kre simir Josi,et al.  Synchronization of Chaotic Systems and Invariant Manifolds , 2007 .

[5]  Wu Xiaoqun,et al.  A unified chaotic system with continuous periodic switch , 2004 .

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

[7]  Zhang Suo-chun,et al.  Controlling uncertain Lü system using backstepping design , 2003 .

[8]  Alexey A Koronovskii,et al.  Generalized synchronization: a modified system approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Xinghuo Yu,et al.  Chaos Synchronization via Controlling Partial State of Chaotic Systems , 2001, Int. J. Bifurc. Chaos.

[10]  Yao-Chen Hung,et al.  Synchronization of two different systems by using generalized active control , 2002 .

[11]  Daolin Xu,et al.  Controlled Projective Synchronization in Nonpartially-Linear Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[12]  Mohammad Ali Khan,et al.  Three control strategies for unified chaotic system , 2011 .

[13]  Jinhu Lu,et al.  Synchronization of an uncertain unified chaotic system via adaptive control , 2002 .

[14]  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.

[15]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .

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

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

[18]  Swarup Poria,et al.  Synchronization of bidirectionally coupled chaotic Chen's system with delay , 2009 .

[19]  Olga I. Moskalenko,et al.  Generalized synchronization onset , 2005, nlin/0512044.