Generalized synchronization of chaos in autonomous systems

Abstract

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables nor it needs to be active for all times for achieving generalized synchronization. The procedure is based on the analogy between a response map subject to an external drive acting with a probability p and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems.

5 pages, 7 figures, accepted in PRE

References in corpus (4)

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• Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps
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Cited by in corpus (8)

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• Collective behavior of chaotic oscillators with environmental coupling
• Equivalent synchronization of chaos in driven and in autonomous systems
• Synchronization induced by intermittent versus partial drives in chaotic systems
• The role of intermediaries in the synchronization of pulse-coupled oscillators