2020/10/31 by Can Xu, Per Sebastian Skardal
Computer Science · Engineering · Neuroscience · Physics and Astronomy · #Distribution (mathematics) #Kuramoto model #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Population #Population model #Spectrum (functional analysis) #Stability (learning theory) #Stability and Controllability of Differential Equations #Synchronization (alternating current) #Variety (cybernetics) #nlin.AO
paper · pdf · doi:10.1103/physrevresearch.3.013013
published as Phys. Rev. Research 3, 013013 (2021)
arxiv created 2020/12/28 · openalex created_date 2021/01/05 · openalex publication_date 2021/01/07 · arxiv updated 2021/01/13 · openalex updated_date 2026/08/05
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., nonadditive, 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.