Detecting phase synchronization by localized maps: Application to neural networks

TL;DR

This paper introduces a method to detect phase synchronization in coupled chaotic oscillators and neural networks by analyzing localized maps at specific times, without directly measuring phase.

Contribution

The paper presents a novel approach using localized maps to identify phase synchronization in systems where phase measurement is difficult or impossible.

Findings

Effective detection of phase synchronization without phase measurement

Application to neural networks with non-identical neurons

Successful analysis of synchronization onset in chaotic systems

Abstract

We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether this set of points is localized. In particular, we show that this approach is fruitful to analyze the onset of phase synchronization in chaotic attractors whose phases are not well defined, as well as, in networks of non-identical spiking/bursting neurons connected by chemical synapses.