Dynamics of Noisy Oscillator Populations beyond the Ott-Antonsen Ansatz

Physical Review Letters
Irina V TyulkinaArkady Pikovsky

Abstract

We develop an approach for the description of the dynamics of large populations of phase oscillators based on "circular cumulants" instead of the Kuramoto-Daido order parameters. In the thermodynamic limit, these variables yield a simple representation of the Ott-Antonsen invariant solution [E. Ott and T. M. Antonsen, Chaos 18, 037113 (2008)CHAOEH1054-150010.1063/1.2930766] and appear appropriate for constructing perturbation theory on top of the Ott-Antonsen ansatz. We employ this approach to study the impact of small intrinsic noise on the dynamics. As a result, a closed system of equations for the two leading cumulants, describing the dynamics of noisy ensembles, is derived. We exemplify the general theory by presenting the effect of noise on the Kuramoto system and on a chimera state in two symmetrically coupled populations.

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Citations

Nov 6, 2018·Chaos·Denis S GoldobinArkady Pikovsky
May 29, 2020·Journal of Mathematical Neuroscience·Christian BickErik A Martens
Oct 24, 2019·Physical Review. E·Franziska PeterArkady Pikovsky
Jan 23, 2020·Physical Review. E·Chen Chris Gong, Arkady Pikovsky
Jun 18, 2020·Frontiers in Computational Neuroscience·Marco SegneriAlessandro Torcini
Apr 14, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Irina V TyulkinaYuriy L Raikher
Nov 21, 2020·Physical Review. E·Takuma Tanaka
Dec 18, 2020·Physical Review. E·Marzena CiszakSimona Olmi
Jan 6, 2021·Nature Communications·Ralf TönjesTiago Pereira
Apr 16, 2021·Nature·Michel FruchartVincenzo Vitelli
Jun 18, 2021·Physical Review. E·Carlo R Laing
Jul 31, 2021·Physical Review Letters·Denis S GoldobinAlessandro Torcini
Aug 4, 2021·Chaos·Rico BernerEckehard Schöll
Aug 4, 2021·Chaos·Thomas N ThiemIoannis G Kevrekidis

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