Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions

Abstract

Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order interactions between three or more units) continues to grow we study an extension of the Kuramoto model where oscillators are coupled via three-way interactions that exhibits novel dynamical properties including clustering, multistability, and abrupt desynchronization transitions. Here we provide a rigorous description of the stability of various multicluster states by studying their spectral properties in the thermodynamic limit. Not unlike the classical Kuramoto model, a natural frequency distribution with infinite support yields a population of drifting oscillators, which in turn guarantees that a portion of the spectrum is located on the imaginary axes, resulting in neutrally stable or unstable solutions. On the other hand, a natural frequency distribution with finite support allows for a fully phase-locked state, whose spectrum is real and may be linearly stable or unstable.

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Cited by in corpus (8)

• Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
• Multistability in coupled oscillator systems with higher-order interactions and community structure
• Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
• Collective dynamics on higher-order networks
• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
• Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions