Affiliation:
1. Instituto de Física de Cantabria (IFCA), Universidad de Cantabria-CSIC, Avda. Los Castros, s/n, 39005 Santander, Spain
Abstract
The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott–Antonsen theory can be applied, and the heterogeneity is distributed following a rational function. In this work, we demonstrate the usefulness of a moment-based scheme to reproduce the dynamics of infinitely many oscillators. Our analysis is particularized for Gaussian heterogeneities, leading to a Fourier–Hermite decomposition of the oscillator density. The Fourier–Hermite moments obey a set of hierarchical ordinary differential equations. As a preliminary experiment, the effects of truncating the moment system and implementing different closures are tested in the analytically solvable Kuramoto model. The moment-based approach proves to be much more efficient than the direct simulation of a large oscillator ensemble. The convenience of the moment-based approach is exploited in two illustrative examples: (i) the Kuramoto model with bimodal frequency distribution, and (ii) the “enlarged Kuramoto model” (endowed with nonpairwise interactions). In both systems, we obtain new results inaccessible through direct numerical integration of populations.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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1. Introduction to Focus Issue: Dynamics of oscillator populations;Chaos: An Interdisciplinary Journal of Nonlinear Science;2023-01-01