Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations

Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations

A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize the pha...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2018-04, Vol.28 (4), p.045103-045103
Hauptverfasser: Nakao, Hiroya, Yasui, Sho, Ota, Masashi, Arai, Kensuke, Kawamura, Yoji
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container_issue 4
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container_title Chaos (Woodbury, N.Y.)
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creator Nakao, Hiroya
Yasui, Sho
Ota, Masashi
Arai, Kensuke
Kawamura, Yoji
description A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize the phase response of the collective oscillation to small perturbations applied to individual elements, is derived. Using the phase sensitivity functions, collective oscillation of the network under weak perturbation can be described approximately by a one-dimensional phase equation. As an example, mutual synchronization between a pair of collectively oscillating networks of excitable and oscillatory FitzHugh-Nagumo elements with random coupling is studied.
doi_str_mv 10.1063/1.5009669
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title Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations
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