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

Hiroya Nakao; Sho Yasui; Masashi Ota; Kensuke Arai; Yoji Kawamura

doi:10.1063/1.5009669

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

Chaos. 2018 Apr;28(4):045103. doi: 10.1063/1.5009669.

Authors

Hiroya Nakao¹, Sho Yasui², Masashi Ota², Kensuke Arai³, Yoji Kawamura⁴

Affiliations

¹ Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
² Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
³ Department of Statistics and Mathematics, Boston University, Boston, Massachusetts 02215, USA.
⁴ Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan.

PMID: 31906627
DOI: 10.1063/1.5009669

Abstract

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.