Complete synchronization of the noise-perturbed Chua's circuits.

In this paper, complete synchronization between unidirectionally coupled Chua's circuits within stochastic perturbation is investigated. Sufficient conditions of complete synchronization between these noise-perturbed circuits are established by means of the so-called LaSalle-type invariance principle for stochastic differential equations. Specific examples and their numerical simulations are also provided to demonstrate the feasibility of these conditions. Furthermore, the results obtained for the coupled Chua's circuits are further generalized to the wide class of coupled systems within stochastic perturbation.

[1]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach , 1983 .

[2]  J. Yorke,et al.  Fractal Basin Boundaries, Long-Lived Chaotic Transients, And Unstable-Unstable Pair Bifurcation , 1983 .

[3]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[4]  Leon O. Chua CHAOS IN NONLINEAR ELECTRONIC CIRCUITS , 1986 .

[5]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[6]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

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

[8]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[9]  L. Arnold Stochastic Differential Equations: Theory and Applications , 1992 .

[10]  Leon O. Chua,et al.  EXPERIMENTAL CHAOS SYNCHRONIZATION IN CHUA'S CIRCUIT , 1992 .

[11]  Leon O. Chua,et al.  Chaos Synchronization in Chua's Circuit , 1993, J. Circuits Syst. Comput..

[12]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[13]  Pikovsky Comment on "Chaos, noise, and synchronization" , 1994, Physical review letters.

[14]  Maritan,et al.  Maritan and Banavar reply. , 1994, Physical review letters.

[15]  Freund,et al.  Chaos, noise, and synchronization reconsidered. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[17]  Gang Hu,et al.  Synchronization of a one-dimensional array of Chua's circuits by feedback control and noise , 1995 .

[18]  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.

[19]  Malescio Noise and synchronization in chaotic systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[22]  P. Gade,et al.  The origin of non-chaotic behavior in identically driven systems , 1995, chao-dyn/9505007.

[23]  Longa,et al.  Roundoff-induced coalescence of chaotic trajectories. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  J. Kurths,et al.  Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization , 1997 .

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

[26]  Vicente Pérez-Muñuzuri,et al.  ANALYSIS OF SYNCHRONIZATION OF CHAOTIC SYSTEMS BY NOISE: AN EXPERIMENTAL STUDY , 1997 .

[27]  Michael Peter Kennedy,et al.  The role of synchronization in digital communications using chaos. I . Fundamentals of digital communications , 1997 .

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

[29]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[30]  Mark Hess,et al.  TRANSITION TO PHASE SYNCHRONIZATION OF CHAOS , 1998 .

[31]  Michael Peter Kennedy,et al.  The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization , 1998 .

[32]  Heinz G. Schuster,et al.  Handbook of Chaos Control: SCHUSTER:HDBK.CHAOS CONTR O-BK , 1999 .

[33]  X. Mao LaSalle-Type Theorems for Stochastic Differential Delay Equations , 1999 .

[34]  M. Newman,et al.  Mean-field solution of the small-world network model. , 1999, Physical review letters.

[35]  E. Sánchez,et al.  Chaotic synchronization in small assemblies of driven Chua's circuits , 2000 .

[36]  Newton G. Bretas,et al.  On the invariance principle: generalizations and applications to synchronization , 2000 .

[37]  E. Platen,et al.  Strong discrete time approximation of stochastic differential equations with time delay , 2000 .

[38]  Kim,et al.  Synchronization in a system of globally coupled oscillators with time delay , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[40]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[41]  Xiaofan Wang,et al.  Generating chaos in Chua's circuit via time-delay feedback , 2001 .

[42]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[43]  K. Shore,et al.  Inverse anticipating chaos synchronization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Guo-Ping Jiang,et al.  A Global Synchronization Criterion for Coupled Chaotic Systems via Unidirectional Linear Error Feedback Approach , 2002, Int. J. Bifurc. Chaos.

[45]  X. Mao A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[46]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[47]  X. Mao,et al.  Numerical solutions of stochastic differential delay equations under local Lipschitz condition , 2003 .

[48]  Guanrong Chen,et al.  On feedback-controlled synchronization of chaotic systems , 2003, Int. J. Syst. Sci..

[49]  P. K. Roy,et al.  Experimental observation on the effect of coupling on different synchronization phenomena in coupled nonidentical Chua’s oscillators , 2003 .

[50]  Jaroslav Stark,et al.  Chaos: Useful at Last? , 2003, Science.

[51]  Xinghuo Yu,et al.  Chaos control : theory and applications , 2003 .

[52]  Erik M. Bollt,et al.  Review of Chaos Communication by Feedback Control of Symbolic Dynamics , 2003, Int. J. Bifurc. Chaos.

[53]  E. M. Shahverdiev,et al.  Generalized synchronization in time-delayed systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Maosheng Wang,et al.  Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators , 2005 .

[55]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .