Adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters

This work investigates the adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q–S synchronization of two different chaotic systems (including different dimensional systems) are derived, based on Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the non-identical chaotic systems are to have Q–S synchronization. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

[1]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .

[2]  Guanrong Chen,et al.  Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Simin Yu,et al.  Generating hyperchaotic Lü attractor via state feedback control , 2006 .

[4]  Q. Jia.  Projective synchronization of a new hyperchaotic Lorenz system , 2007 .

[5]  K. Wong,et al.  Noise and synchronization in chaotic neural networks , 1998 .

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

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

[8]  Henry Leung,et al.  Experimental verification of multidirectional multiscroll chaotic attractors , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Chuandong Li,et al.  Lag synchronization of hyperchaos with application to secure communications , 2005 .

[10]  M. M. El-Dessoky,et al.  Adaptive synchronization of a hyperchaotic system with uncertain parameter , 2006 .

[11]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[12]  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.

[13]  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.

[14]  Rong Zhang,et al.  Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems , 2007 .

[15]  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.

[16]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[17]  Zhi-Hong Guan,et al.  Adaptive synchronization between two different hyperchaotic systems , 2008 .

[18]  Zhenyuan Xu,et al.  A general scheme for Q-S synchronization of chaotic systems , 2008 .

[19]  Mohd. Salmi Md. Noorani,et al.  Chaos Anti-synchronization between Two Novel Different Hyperchaotic Systems , 2008 .

[20]  Ma Jun,et al.  Control Chaos in Hindmarsh—Rose Neuron by Using Intermittent Feedback with One Variable , 2008 .

[21]  Zhenya Yan,et al.  Chaos Q–S synchronization between Rössler system and the new unified chaotic system , 2005 .

[22]  Yong Chen,et al.  Generalized Q-S (lag, anticipated and complete) synchronization in modified Chua's circuit and Hindmarsh-Rose systems , 2006, Appl. Math. Comput..