Early detection of synchrony in coupled oscillator model

TL;DR

This paper investigates an early warning index based on mutual information to detect transitions to synchronization in coupled oscillators, demonstrating its effectiveness across different control parameters and network configurations.

Contribution

It introduces an early warning index explicitly dependent on mutual information that signals impending synchronization transitions in coupled oscillator systems.

Findings

Early warning index reaches distinct values before synchronization occurs.

The index is effective across different control parameters and network sizes.

Transitions involve a shift to periodic or chaotic dynamics depending on the control parameter.

Abstract

In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling strength as the required control parameters. The coupled oscillator models are widely used and well-documented for studying various aspects of nature. However, the early warning index used in this paper is an explicit function of the mutual information of the coupled oscillators and reaches two different values before the interacting oscillators yield complete and generalized synchronizations. The transitions to synchrony using the unconventional control parameter are associated with a transition to periodic dynamics of the individual oscillators from their initial chaotic dynamics. Besides, when we use the coupling strength as a control parameter, the interacting oscillator exhibits chaotic dynamics during the synchronizations. Our analysis mainly involves different examples of two low-dimensional oscillators. Finally, we extend our study to a network of interacting oscillators. The applicability of the early detection index is verified in all cases.