Symmetric States Requiring System Asymmetry

TL;DR

This paper reveals that in certain complex systems, stable synchronization of identical oscillators can require intentionally breaking system symmetry through parameter diversity, challenging traditional symmetry-breaking notions.

Contribution

It introduces the novel concept that system asymmetry can be necessary for the stability of symmetric states in coupled oscillators.

Findings

Stable synchronization can require nonidentical oscillator parameters.

Diversity among oscillators can facilitate uniformity and consensus.

Symmetry can be preserved through intentional asymmetry.

Abstract

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here we report on the discovery of the converse of symmetry breaking--the scenario in which complete synchronization is not stable for identically-coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.