Finite-size effects in a stochastic Kuramoto model

2017/09/08 by Georg A. Gottwald, Gottwald, Georg A. · 1 citation
Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #math.DS #math.PR #nlin.AO

paper · pdf · doi:10.48550/arxiv.1709.02685

arxiv created 2017/09/08 · arxiv updated 2017/09/11

Abstract

We present a collective coordinate approach to study the collective behaviour of a finite ensemble of N stochastic Kuramoto oscillators using two degrees of freedom; one describing the shape dynamics of the oscillators and one describing their mean phase. Contrary to the thermodynamic limit N→∞ in which the mean phase of the cluster of globally synchronized oscillators is constant in time, the mean phase of a finite-size cluster experiences Brownian diffusion with a variance proportional to 1/N. This finite-size effect is quantitatively well captured by our collective coordinate approach.

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• Finite-size induced random switching of chimeras in a deterministic two-population Kuramoto-Sakaguchi model

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