Using white noise to enhance synchronization of coupled chaotic systems.

In the paper, complete synchronization of two chaotic oscillators via unidirectional coupling determined by white noise distribution is investigated. It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling. The established theoretical result supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators. Furthermore, numerical examples are provided to illustrate some possible applications of the theoretical result.

[1]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[2]  A. Friedman Stochastic Differential Equations and Applications , 1975 .

[3]  O. Rössler An equation for continuous chaos , 1976 .

[4]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[5]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  N. G. van Kampen,et al.  Itô versus Stratonovich , 1981 .

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

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

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

[10]  G. Bard Ermentrout,et al.  Synchronization in a pool of mutually coupled oscillators with random frequencies , 1985 .

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

[12]  R. Lefever,et al.  Noise in nonlinear dynamical systems: Noise-induced transitions , 1989 .

[13]  Alʹbert Nikolaevich Shiri︠a︡ev,et al.  Theory of martingales , 1989 .

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

[15]  Chen,et al.  Transition to chaos for random dynamical systems. , 1990, Physical review letters.

[16]  Lennart Carleson,et al.  The Dynamics of the Henon Map , 1991 .

[17]  Edward Ott,et al.  Fractal distribution of floaters on a fluid surface and the transition to chaos for random maps , 1991 .

[18]  Arkady Pikovsky,et al.  Statistics of trajectory separation in noisy dynamical systems , 1992 .

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

[20]  Celso Grebogi,et al.  Using small perturbations to control chaos , 1993, Nature.

[21]  C. Robinson Dynamical Systems: Stability, Symbolic Dynamics, and Chaos , 1994 .

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

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

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

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

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

[27]  J. M. Sancho,et al.  Noise in spatially extended systems , 1999 .

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

[29]  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.

[30]  Jürgen Kurths,et al.  Noise-enhanced phase synchronization of chaotic oscillators. , 2002, Physical review letters.

[31]  Jürgen Kurths,et al.  Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. , 2002, Physical review letters.

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

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

[34]  Jürgen Kurths,et al.  Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. , 2003, Chaos.

[35]  Ying Zhang,et al.  Experimental investigation of partial synchronization in coupled chaotic oscillators. , 2003, Chaos.

[36]  L. Arnold Random Dynamical Systems , 2003 .

[37]  S Boccaletti,et al.  Noise-enhanced synchronization of homoclinic chaos in a CO2 laser. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[40]  S Boccaletti,et al.  Constructive effects of noise in homoclinic chaotic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[42]  Wei Lin,et al.  Complete synchronization of the noise-perturbed Chua's circuits. , 2005, Chaos.

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

[44]  René Lefever,et al.  Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology , 2007 .

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