Breathing synchronization in interconnected networks

TL;DR

This paper investigates how time delays affect synchronization in interconnected oscillator networks, revealing a novel breathing regime with groups synchronized at different frequencies and phase relationships.

Contribution

It introduces the concept of breathing synchronization in delayed interconnected networks and analyzes how coupling strength and communication lag influence the dynamics.

Findings

Discovery of a breathing synchronization regime with frequency-divided groups

Identification of phase and anti-phase relationships between network groups

Observation of internal synchronization with phase shifts at strong couplings

Abstract

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.