Emergent multistability and frustration in phase-repulsive networks of oscillators

TL;DR

This paper investigates the collective behavior of oscillator networks with phase-repulsive coupling, revealing how network topology influences multistability and frustration in their dynamical states.

Contribution

It introduces the concept of link frustration to quantify network states and demonstrates the dependence of final states on network topology in phase-repulsive oscillator networks.

Findings

Network topology critically affects dynamical states.

Multiple final frustration states exist with unique stability properties.

Total frustration correlates with network structure.

Abstract

We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states. In opposition to widely studied phase-attractive case, the properties of final dynamical states in our model critically depend on the network topology. In particular, each network's total frustration value is intimately related to its topology. Moreover, phase-repulsive networks in general display multiple final frustration states, whose statistical and stability properties are uniquely identifying them.