Limits to detection of generalized synchronization in delay-coupled chaotic oscillators

Hideyuki Kato,Claudio R Mirasso,Miguel C Soriano,Ernesto Pereda,Ingo Fischer

doi:10.1103/physreve.88.062924

Abstract

We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possible. Therefore, in this study, widely used indicators to directly quantify generalized and phase synchronization from noise-free time series of two oscillators are employed complementarily to the auxiliary system approach. In our analysis, none of the indices provide the consistent results of the auxiliary system approach. Our findings indicate that it is a major challenge to directly detect synchronization in a generalized sense between two oscillators that are connected via a chain of other oscillators, even if the oscillators are identical. This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof.

Highlights

Over the past few decades scientists from different disciplines have been trying to identify and quantify synchronization in coupled dynamical systems and a large number of measures have been proposed [1,2]
If brain sites interact via many intermediate neural oscillators as considered in this paper, given time series of a certain length, and with a certain amount of noise, most of the tested indices cannot identify the interactions between the sites, and the connectivity patterns derived from the indices are not reliable
An interesting finding in our analyses of Generalized synchronization (GS) was that only the generalized synchronization index (GSI) and the convergent cross mapping (CCM) exhibit clearly different amplitudes with respect to positive and negative shifts

Summary

Introduction

Over the past few decades scientists from different disciplines have been trying to identify and quantify synchronization in coupled dynamical systems and a large number of measures have been proposed [1,2]. These studies are based on the understanding and knowledge of the complex dynamics in coupled systems. Most of these analyses focused on the study of identical synchronization, in which coupled oscillators follow the same trajectory [3,4]. Another type of synchronization is phase synchronization (PS), in which phases of the oscillators are correlated, while their amplitudes might be uncorrelated

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