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

Hiroya Nakao, Sho Yasui, Masashi Ota, Kensuke Arai, Yoji Kawamura
2018 Chaos  
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
more » ... turbation 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:10.1063/1.5009669 pmid:31906627 fatcat:xoxprnx5mfevjjeeanlwy5prku