General Framework for phase synchronization through localized sets

TL;DR

This paper introduces a novel method to detect phase synchronization in coupled chaotic oscillators by analyzing localized sets formed through event-based observations, applicable even to multi-scale systems.

Contribution

It presents a general framework for identifying phase synchronization without explicit phase measurement, applicable to complex systems like neuronal networks.

Findings

Clusters of phase-synchronous neurons can emerge before full synchronization.

Localized sets relate to the amount of information exchanged.

The method works for oscillators with multiple time scales.

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.