A New Adaptive Chaos Synchronization Principle for a Class of Chaotic Systems

In this paper, we propose a new adaptive synchronization principle to resolve the chaos synchronization of the drive-driven type chaotic systems. An adaptive response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to disturbances and/or some unknown parameters. To guarantee the synchronization between the coupled chaotic oscillators, proper coupling constants are selected by the Lyapunov stability theory and Hurwitz Theorem. Two well-known chaotic systems: Lorenz system and Chua's circuit are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme.

[1]  Classification and Computation of Non-resonant Double Hopf Bifurcations and Solutions in Delayed van der Pol-Duffing System , 2005 .

[2]  Ricardo Femat,et al.  Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization , 2000 .

[3]  M. Bernardo.  An adaptive approach to the control and synchronization of continuous-time chaotic systems , 1996 .

[4]  Qishao Lu,et al.  Generation of Firing Rhythm Patterns and Synchronization in the Morris-Lecar Neuron Model , 2005 .

[5]  M. T. Yassen,et al.  Chaos synchronization between two different chaotic systems using active control , 2005 .

[6]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[8]  X. Shan,et al.  A linear feedback synchronization theorem for a class of chaotic systems , 2002 .

[9]  L. Chua,et al.  Canonical realization of Chua's circuit family , 1990 .

[10]  Leon O. Chua,et al.  ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS , 1996 .

[11]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[12]  Chaotifying a Linear Time-Invariant System by the Decentralized State Feedback Controller and Sine Function , 2004 .

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

[14]  Ju H. Park.  Chaos synchronization of a chaotic system via nonlinear control , 2005 .

[15]  Jun-Guo Lu,et al.  Linear generalized synchronization of continuous-time chaotic systems , 2003 .

[16]  Gonzalo Alvarez,et al.  Breaking projective chaos synchronization secure communication using filtering and generalized synchronization , 2004, Chaos, Solitons & Fractals.

[17]  Jin Zhou,et al.  A New Synchronization Principle and Application to Chua's Circuits , 2002, Int. J. Bifurc. Chaos.

[18]  Wei Xing Zheng,et al.  An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems , 2005 .

[19]  Yen-Sheng Chen,et al.  Nonlinear Dynamics and Chaos Control for a Time Delay Duffing System , 2005 .

[20]  Boris R. Andrievsky.  Adaptive synchronization methods for signal transmission on chaotic carriers , 2002, Math. Comput. Simul..

[21]  Moez Feki,et al.  Observer-based chaotic synchronization in the presence of unknown inputs , 2003 .

[22]  T. Liao,et al.  Adaptive Synchronization of Two Lorenz Systemsfn1 , 1998 .

[23]  H. Agiza,et al.  Controlling and Synchronization of Rossler System with Uncertain Parameters , 2004 .

[24]  Wuyin Jin,et al.  Stochastic Synchronization and Aperiodic Stochastic Resonance of a Unidirectionally Coupled Single-mode Optical System , 2005 .

[25]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[26]  Hsien-Keng Chen,et al.  Global chaos synchronization of new chaotic systems via nonlinear control , 2005 .

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

[28]  Zheng-Ming Ge,et al.  Chaos synchronization and parameter identification of three time scales brushless DC motor system , 2005 .

[29]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .

[30]  Er-Wei Bai,et al.  Synchronization and Control of Chaotic Systems , 1999 .

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

[32]  Samuel Bowong,et al.  Synchronization of uncertain chaotic systems via backstepping approach , 2004 .