Continua and persistence of periodic orbits in ensembles of oscillators

Author:

Ronge R,Zaks M A,Pereira T

Abstract

Abstract Certain systems of coupled identical oscillators like the Kuramoto–Sakaguchi or the active rotator model possess the remarkable property of being Watanabe–Strogatz integrable. We prove that such systems, which couple via a global order parameter, feature a normally attracting invariant manifold that is foliated by periodic orbits. This allows us to study the asymptotic dynamics of general ensembles of identical oscillators by applying averaging theory. For the active rotator model, perturbations result in only finitely many persisting orbits, one of them giving rise to splay state dynamics. This sheds some light on the persistence and typical behavior of splay states previously observed.

Funder

Royal Society

Fundação de Amparo à Pesquisa do Estado de São Paulo

Deutsche Forschungsgemeinschaft

Publisher

IOP Publishing

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