Generalized Cascade Synchronization of Discrete-time Henon-like Map

This Letter addresses the generalized cascade synchronization problem of discrete-time hyperchaotic systems. By choosing a general kind of proportional scaling error functions and based on rigorous control theory, we take the discrete-time Henon-like map as a example to achieve the generalized cascade synchronization. Numerical simulations are used to show the effectiveness of the proposed technique.

[1]  Michael Peter Kennedy,et al.  Chaotic Modulation for Robust Digital Communications over Multipath Channels , 2000, Int. J. Bifurc. Chaos.

[2]  Louis M. Pecora,et al.  Cascading synchronized chaotic systems , 1993 .

[3]  Henk Nijmeijer Control of chaos and synchronization , 1997 .

[4]  Edward Ott Chaos in Dynamical Systems: Control and synchronization of chaos , 2002 .

[5]  Thongchai Botmart,et al.  Adaptive control and synchronization of the perturbed Chua's system , 2007, Math. Comput. Simul..

[6]  Leon O. Chua,et al.  Conditions for impulsive Synchronization of Chaotic and hyperchaotic Systems , 2001, Int. J. Bifurc. Chaos.

[7]  Jinhu Lu,et al.  Chaos synchronization between linearly coupled chaotic systems , 2002 .

[8]  Jitao Sun,et al.  Impulsive control and synchronization for a new chaotic system , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[9]  Jinhu Lu,et al.  Controlling uncertain Lü system using linear feedback , 2003 .

[10]  Yong Chen,et al.  The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems , 2008, Appl. Math. Comput..

[11]  Z. Guan,et al.  Generalized synchronization of continuous chaotic system , 2006 .

[12]  Juergen Kurths,et al.  Introduction: Control and synchronization in chaotic dynamical systems. , 2003, Chaos.

[13]  D. Hitzl,et al.  An exploration of the Hénon quadratic map , 1985 .

[14]  Ju H. Park Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[15]  W. Ditto,et al.  Introduction: Control and synchronization of chaos. , 1997, Chaos.

[16]  H. An,et al.  The function cascade synchronization method and applications , 2008 .

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

[18]  R. Massey From chaos to order? , 1986, Connecticut medicine.

[19]  Zheng Zhi-Gang,et al.  Synchronized Firing in Coupled Inhomogeneous Excitable Neurons , 2002 .

[20]  Jianping Yan,et al.  Generalized projective synchronization of chaos: The cascade synchronization approach , 2006 .

[21]  Guohui Li,et al.  Generalized projective synchronization between Lorenz system and Chen’s system , 2007 .

[22]  Louis M. Pecora,et al.  Fundamentals of synchronization in chaotic systems, concepts, and applications. , 1997, Chaos.

[23]  Zhenya Yan,et al.  Q-S synchronization in 3D Hénon-like map and generalized Hénon map via a scalar controller , 2005 .

[24]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[25]  Zhenya Yan,et al.  Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach. , 2006, Chaos.

[26]  Jitao Sun,et al.  Impulsive control and synchronization of Chua's oscillators , 2004, Math. Comput. Simul..

[27]  Jitao Sun,et al.  Impulsive control of a new chaotic system , 2004, Math. Comput. Simul..

[28]  Luo Runzi,et al.  Impulsive control and synchronization of a new chaotic system , 2008 .

[29]  Lilian Huang,et al.  Parameters identification and adaptive synchronization of chaotic systems with unknown parameters , 2005 .

[30]  Guohui Li Modified projective synchronization of chaotic system , 2007 .