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Generalized synchronization of identical chaotic systems on the route from an independent dynamics to the complete synchrony

Generalized synchronization of identical chaotic systems on the route from an independent... The transition from asynchronous hyperchaos to complete synchrony in coupled identical chaotic systems may either occur directly or be mediated by a preliminary stage of generalized synchronization. In the present paper we investigate the underlying mechanisms of realization of the both scenarios. It is shown that a generalized synchronization arises when the manifold of identically synchronous states M is transversally unstable, while the local transversal contraction of phase volume first appears in the areas of phase space separated from M and being visited by the chaotic trajectories. On the other hand, a direct transition from an asynchronous hyperchaos to the complete synchronization occurs, under variation of the controlling parameter, if the transversal stability appears first on the manifold M, and only then it extends upon the neighboring phase volume. The realization of one or another scenario depends upon the choice of the coupling function. This result is valid for both unidirectionally and mutually coupled systems, that is confirmed by theoretical analysis of the discrete models and numerical simulations of the physically realistic flow systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Generalized synchronization of identical chaotic systems on the route from an independent dynamics to the complete synchrony

Regular and Chaotic Dynamics , Volume 18 (3) – Jun 2, 2013

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References (32)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354713030027
Publisher site
See Article on Publisher Site

Abstract

The transition from asynchronous hyperchaos to complete synchrony in coupled identical chaotic systems may either occur directly or be mediated by a preliminary stage of generalized synchronization. In the present paper we investigate the underlying mechanisms of realization of the both scenarios. It is shown that a generalized synchronization arises when the manifold of identically synchronous states M is transversally unstable, while the local transversal contraction of phase volume first appears in the areas of phase space separated from M and being visited by the chaotic trajectories. On the other hand, a direct transition from an asynchronous hyperchaos to the complete synchronization occurs, under variation of the controlling parameter, if the transversal stability appears first on the manifold M, and only then it extends upon the neighboring phase volume. The realization of one or another scenario depends upon the choice of the coupling function. This result is valid for both unidirectionally and mutually coupled systems, that is confirmed by theoretical analysis of the discrete models and numerical simulations of the physically realistic flow systems.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Jun 2, 2013

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