Quasi regular concentric waves in heterogeneous lattices of coupled oscillators

TL;DR

This paper investigates how quenched disorder in heterogeneous lattices of coupled oscillators can induce and enhance regular concentric wave patterns, especially near the synchronization threshold, through symmetry-breaking mechanisms.

Contribution

It reveals that disorder can promote regular wave formation in coupled oscillators and provides a theoretical explanation for this phenomenon.

Findings

Maximal wave regularity occurs at the edge of synchronization.

Disorder induces and increases the regularity of concentric waves.

The emergence of waves is linked to symmetry breaking of the interaction function.

Abstract

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.