General Framework for phase synchronization through localized sets

Abstract

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange.

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• Chaotic Phase Synchronization in Bursting-neuron Models Driven by a Weak Periodic Force
• Control and Observability Aspects of Phase Synchronization
• Dynamic environment coupling induce synchronized states in coupled time-delayed electronic circuits
• Transmission of information and synchronization in a pair of coupled chaotic circuits: an experimental overview
• Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems
• Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits
• Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems
• Chaotic, informational and synchronous behaviour of multiplex networks