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

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.

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• Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
• Higher-order interactions induce anomalous transitions to synchrony
• Collective dynamics on higher-order networks
• Opinion disparity in hypergraphs with community structure
• Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models
• Network stochastic resonance under higher-order interactions