Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability

Autor(es)

Vlasov, Vladimir ^{[1, 2]} ; Rosenblum, Michael ^[1] ; Pikovsky, Arkady ^{[1, 3]}

Afiliação do(s) autor(es)

^[1] Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam - Germany

^[2] Ist Italiano Tecnol, Ctr Neurosci & Cognit Syst, Corso Bettini 31, I-38068 Rovereto - Italy

^[3] Nizhnii Novgorod State Univ, Dept Control Theory, Gagarin Ave 23, Nizhnii Novgorod 606950 - Russia

• Tipo de documento: Artigo Científico
• Fonte: Journal of Physics A-Mathematical and Theoretical; v. 49, n. 31 AUG 5 2016.
• Citações Web of Science: 3

Resumo

As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations. (AU)

• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Linha de fomento: Auxílio à Pesquisa - Temático