Multistable attractors in a network of phase oscillators with three-body interaction

TL;DR

This paper explores how three-body interactions in phase oscillator networks lead to infinite multistability of synchronized states, affecting the system's long-term dynamics and degree of synchrony.

Contribution

It introduces a model of phase oscillators with three-body interactions and demonstrates the emergence of infinite multistable synchronized states both numerically and theoretically.

Findings

Infinite multistable synchronized states appear above a critical coupling strength.

A stable incoherent state exists at all coupling strengths.

The degree of synchrony varies continuously depending on initial conditions.

Abstract

Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with three-body interaction. As a result, an infinite number of multistable synchronized states appear above a critical coupling strength, while a stable incoherent state always exists for any coupling strength. Owing to the infinite multistability, the degree of synchrony in asymptotic state can vary continuously within some range depending on the initial phase pattern.