Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

[1]  Rajarshi Roy,et al.  Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Krešimir Josić,et al.  INVARIANT MANIFOLDS AND SYNCHRONIZATION OF COUPLED DYNAMICAL SYSTEMS , 1998 .

[3]  Chen Long,et al.  Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system , 2010 .

[4]  Gauthier,et al.  Intermittent Loss of Synchronization in Coupled Chaotic Oscillators: Toward a New Criterion for High-Quality Synchronization. , 1996, Physical review letters.

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

[6]  Guanrong Chen,et al.  Using white noise to enhance synchronization of coupled chaotic systems. , 2006, Chaos.

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

[8]  Jia Lixin,et al.  A new four-dimensional hyperchaotic Chen system and its generalized synchronization , 2010 .

[9]  T. Ma,et al.  APPLICATION OF ADAPTIVE MESH REFINEMENT IN NUMERICAL SIMULATION OF GAS DETONATION , 2010 .

[10]  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.

[11]  TianBao Ma,et al.  Influence of obstacle disturbance in a duct on explosion characteristics of coal gas , 2010 .

[12]  E. Hille,et al.  Lectures on ordinary differential equations , 1968 .

[13]  Hölder continuity of two types of generalized synchronization manifold. , 2008, Chaos.

[14]  刘玉金,et al.  Chaos synchronization in injection-locked semiconductor lasers with optical feedback , 2007 .

[15]  M G Cosenza,et al.  Generalized synchronization of chaos in autonomous systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Atsushi Uchida,et al.  Generalized synchronization of chaos in identical systems with hidden degrees of freedom. , 2003, Physical review letters.

[17]  T. Ye,et al.  Equation Chapter 1 Section 1 Propagation Mechanism of Non-steady Gaseous Detonation , 2008 .

[18]  Krešimir Josić,et al.  Synchronization of chaotic systems and invariant manifolds , 2000 .

[19]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.