2017/06/30 by David J. Jörg, David J Jörg
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Computer science #Discretization #Kuramoto model #Markov chain #Mathematical analysis #Mathematics #Maxima and minima #Multistability #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Observable #Phase (matter) #Phase synchronization #Physics #Quantum mechanics #Rendering (computer graphics) #Statistical physics #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.96.032201
published as Phys. Rev. E 96, 032201 (2017) · 14 pages, 8 figures
arxiv created 2017/09/01 · openalex publication_date 2017/09/01 · arxiv updated 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.