Driven Maps and the Emergence of Ordered Collective Behavior in Globally Coupled Maps

Abstract

A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an external drive. A vector field which results from this analogy appears to govern the transient evolution of the globally coupled system. General forms of global couplings are considered. Some simple applications are given.

5 pages, 6 figs; submitted to PRL

Cited by in corpus (12)

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• Very long transients in globally coupled maps
• Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters
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• Generalized synchronization of chaos in autonomous systems
• Chimeras and clusters in networks of hyperbolic chaotic oscillators
• Global interactions, information flow, and chaos synchronization
• Emergence of patterns in driven and in autonomous spatiotemporal systems
• Cluster dynamics in systems with constant mean field coupling
• Asymmetric cluster and chimera dynamics in globally coupled systems
• Equivalent synchronization of chaos in driven and in autonomous systems
• Chaos synchronization with coexisting global fields