Synchronisation Induced by Repulsive Interactions in a System of van der Pol Oscillators

TL;DR

This paper investigates how repulsive interactions in a system of identical van der Pol oscillators influence synchronization, revealing that intermediate levels of repulsion can induce macroscopic oscillations and affect response to external signals.

Contribution

It introduces the effect of competitive repulsive interactions on synchronization in coupled van der Pol oscillators, highlighting their role in emergent macroscopic oscillations.

Findings

Intermediate repulsive links induce macroscopic oscillations.

Competitive interactions alter synchronization properties.

Repulsive links can enable oscillators to respond to weak external signals.

Abstract

We consider a system of identical van der Pol oscillators, globally coupled through their velocities, and study how the presence of competitive interactions affects its synchronisation properties. We will address the question from two points of view. Firstly, we will investigate the role of competitive interactions on the synchronisation among identical oscillators. Then, we will show that the presence of an intermediate fraction of repulsive links results in the appearance of macroscopic oscillations at that signal's rhythm, in regions where the individual oscillator is unable to synchronise with a weak external signal.