Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach.

First, a type of Q-S (complete or anticipated) synchronization is defined in discrete-time dynamical systems. Second, based on backstepping design with a scalar controller, a systematic, concrete and automatic scheme is presented to investigate Q-S (complete or anticipated) synchronization between the discrete-time drive system and response system with strict-feedback form. Finally, the proposed scheme is used to illustrate Q-S (complete or anticipated) synchronization between the two-dimensional discrete-time Lorenz system and Fold system, as well as the three-dimensional hyperchaotic discrete-time Rossler system and generalized discrete-time Rossler system. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. Our scheme can be also extended to investigate Q-S (complete or anticipated) synchronization between other discrete-time dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller and to verify its effectiveness in computer.

[1]  Zhenya Yan,et al.  Q-S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems--a symbolic-numeric computation approach. , 2005, Chaos.

[2]  Mao Wang,et al.  Synchronization of generalized Henon map via backstepping design , 2005 .

[3]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[4]  Arne Beeker,et al.  Scaling and decay in periodically driven scattering systems. , 1993, Chaos.

[5]  Keiji Konishi,et al.  Observer-based delayed-feedback control for discrete-time chaotic systems , 1998 .

[6]  P. Kokotovic,et al.  Adaptive control of a class of nonlinear discrete-time systems , 1995 .

[7]  G. Zaslavsky,et al.  Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamics. , 1997, Chaos.

[8]  N. Rulkov.  Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[9]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[10]  Leon O. Chua,et al.  Equivalent CNN Cell Models and Patterns , 2003, Int. J. Bifurc. Chaos.

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

[12]  K. Stefanski.  Modelling chaos and hyperchaos with 3-D maps , 1998 .

[13]  Makoto Itoh,et al.  Chaos Synchronization in Discrete-Time Dynamical Systems and Its Applications , 1994 .

[14]  Xiaofan Wang,et al.  Backstepping control of discrete-time chaotic systems with application to the Henon system , 2001 .

[15]  S Boccaletti,et al.  Unifying framework for synchronization of coupled dynamical systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[17]  Adi R. Bulsara,et al.  Signal enhancement in a r.f. SQUID using stochastic resonance , 1995 .

[18]  Shuzhi Sam Ge,et al.  Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems , 2003, Autom..

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

[20]  G. Baier,et al.  Maximum hyperchaos in generalized Hénon maps , 1990 .

[21]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[22]  Xiao-Song Yang,et al.  A framework for synchronization theory , 2000 .

[23]  Zhenya Yan,et al.  A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems. , 2005, Chaos.

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

[25]  Shuzhi Sam Ge,et al.  Adaptive backstepping Control of uncertain Lorenz System , 2001, Int. J. Bifurc. Chaos.

[26]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[27]  S. Ge,et al.  Adaptive synchronization of uncertain chaotic systems via backstepping design , 2001 .

[28]  Ljupco Kocarev,et al.  A unifying definition of synchronization for dynamical systems. , 1998, Chaos.

[29]  Frank Moss,et al.  Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance , 1993, Nature.

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