2014/04/29 by Maxim Komarov, M. Komarov, Arkady Pikovsky +1 · 2 citations
Computer Science · Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Asynchronous communication #Combinatorics #Computer science #Coupling (piping) #Entrainment (biomusicology) #Function (biology) #Harmonic #Harmonic oscillator #Kuramoto model #Limit (mathematics) #Mathematical analysis #Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Physics #Quantum mechanics #Slime Mold and Myxomycetes Research #Statistical physics #Synchronization (alternating current) #Topology (electrical circuits) #nlin.AO #nlin.CD
paper · pdf · doi:10.1016/j.physd.2014.09.002
arxiv created 2014/04/29 · openalex publication_date 2014/09/16 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complex order parameters, both for single-branch (one possible state of locked oscillators) and multi-branch (two possible values of locked phases) entrainment. We show that synchronous states coexist with the neutrally linearly stable asynchronous regime. The latter has a finite life time for finite ensembles, this time grows with the ensemble size as a power law.