Multistability in coupled oscillator systems with higher-order interactions and community structure

TL;DR

This paper investigates how higher-order interactions combined with community structure in coupled oscillator systems lead to diverse multistable synchronization states, including novel skew-phase states, supported by bifurcation and stability analyses.

Contribution

It introduces the emergence of new multistable states in coupled oscillators due to the interplay of higher-order interactions and community structure, extending previous models.

Findings

Discovery of new synchronized states with in-phase, anti-phase, and skew-phase community organization

Identification of strong multistability with multiple stable states coexisting

Derivation of low-dimensional dynamics and bifurcation analysis confirming stability of states

Abstract

We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by either higher-order interactions or community structure alone, including synchronized states with communities organized into clusters in-phase, anti-phase, and a novel skew-phase, as well as an incoherent-synchronized state. Moreover, the system displays a strong multistability, with many of these states stable at the same time. We demonstrate our findings by deriving the low dimensional dynamics of the system and examining the system's bifurcations using a stability analysis and perturbation theory.