Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters.

This paper studies the adaptive complete synchronization of chaotic and hyperchaotic systems with fully unknown parameters. In practical situations, some systems' parameters cannot be exactly known a priori, and the uncertainties often affect the stability of the process of synchronization of the chaotic oscillators. An adaptive scheme is proposed to compensate for the effects of parameters' uncertainty based on the structure of chaotic systems in this paper. Based on the Lyapunov stability theorem, an adaptive controller and a parameters update law can be designed for the synchronization of chaotic and hyperchaotic systems. The drive and response systems can be nonidentical, even with different order. Three illustrative examples are given to demonstrate the validity of this technique, and numerical simulations are also given to show the effectiveness of the proposed chaos synchronization method. In addition, this synchronization scheme is quite robust against the effect of noise.

[1]  Ahmed Sadek Hegazi,et al.  Adaptive Synchronization for RÖssler and Chua's Circuit Systems , 2002, Int. J. Bifurc. Chaos.

[2]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[3]  O. Rössler.  An equation for hyperchaos , 1979 .

[4]  Jinhu Lu,et al.  Adaptive synchronization of uncertain Rossler hyperchaotic system based on parameter identification , 2004 .

[5]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[6]  M. T. Yassen,et al.  Adaptive control and synchronization of a modified Chua's circuit system , 2003, Appl. Math. Comput..

[7]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[8]  Debin Huang,et al.  A Simple Adaptive-feedback Controller for Identical Chaos Synchronization , 2022 .

[9]  J García-Ojalvo,et al.  Spatiotemporal communication with synchronized optical chaos. , 2000, Physical review letters.

[10]  Alexey A. Koronovskii,et al.  Synchronization of chaotic oscillator time scales , 2005, nlin/0504049.

[11]  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.

[12]  Oh-Min Kwon,et al.  LMI optimization approach to stabilization of time-delay chaotic systems , 2005 .

[13]  Alexey A. Koronovskii,et al.  Chaotic phase synchronization studied by means of continuous wavelet transform , 2004 .

[14]  Er-Wei Bai,et al.  Synchronization of two Lorenz systems using active control , 1997 .

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

[16]  Carroll,et al.  Synchronous chaos in coupled oscillator systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Guanrong Chen,et al.  Switching manifold approach to chaos synchronization , 1999 .

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

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

[20]  Carroll,et al.  Experimental and Numerical Evidence for Riddled Basins in Coupled Chaotic Systems. , 1994, Physical review letters.

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

[22]  S. Bowong.  Stability analysis for the synchronization of chaotic systems with different order: application to secure communications , 2004 .

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

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

[25]  Er-Wei Bai,et al.  Sequential synchronization of two Lorenz systems using active control , 2000 .

[26]  Alexey A. Koronovskii,et al.  Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators , 2005 .

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

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

[29]  Xinghuo Yu,et al.  An invariant-manifold-based method for chaos control , 2001 .

[30]  D. L. Valladares,et al.  Characterization of intermittent lag synchronization , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  Alexey A Koronovskii,et al.  An approach to chaotic synchronization. , 2004, Chaos.

[32]  Lakshmanan,et al.  Drive-response scenario of chaos synchronization in identical nonlinear systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[34]  Woochang Lim,et al.  Characterization of the noise effect on weak synchronization. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Peng,et al.  Synchronizing hyperchaos with a scalar transmitted signal. , 1996, Physical review letters.

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

[37]  P. V. Popov,et al.  Chaotic synchronization of coupled electron-wave systems with backward waves. , 2005, Chaos.

[38]  Alexey A Koronovskii,et al.  Synchronization of spectral components and its regularities in chaotic dynamical systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[40]  N. Kopell,et al.  Dynamics of two mutually coupled slow inhibitory neurons , 1998 .

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