Evolutionary design of non-frustrated networks of phase-repulsive oscillators

TL;DR

This paper presents an evolutionary algorithm to design bipartite, non-frustrated networks of phase-repulsive oscillators that achieve stable anti-phase synchronization, revealing unique topological features distinct from phase-attractive networks.

Contribution

It introduces a novel evolutionary rewiring method based on link frustration to create non-frustrated, bipartite networks with zero clustering and a clear topological scale.

Findings

Networks are bipartite with zero clustering.

Designed networks achieve stable anti-phase synchronization.

Resulting networks display a distinct topological scale.

Abstract

Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the links with probability proportional to their frustration, until the final network displaying a unique non-frustrated dynamical state is reached. Resulting networks are bipartite and with zero clustering. In addition, the designed non-frustrated anti-phase synchronised networks display a clear topological scale. This contrasts usually studied cases of networks with phase-attractive dynamics, whose performance towards full synchronisation is typically enhanced by the presence of a topological hierarchy.