Geometric signature of complex synchronisation scenarios

TL;DR

This paper introduces a geometric approach using joint recurrence networks to detect and analyze the onset of generalized synchronisation in coupled chaotic oscillators, revealing structural changes in phase space.

Contribution

It presents a novel method linking recurrence network transitivity to synchronization transitions, providing new insights into the geometric signatures of complex coupling.

Findings

Transitivity variations indicate synchronization onset.

Joint recurrence networks reveal structural similarities.

Method applicable to continuous-time chaotic systems.

Abstract

Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled systems including different types of synchronisation such as phase, lag, generalised, or even complete synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful indicator for the emergence of generalised synchronisation. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (Europhys. Lett. 4 (1987), 973).