2017/10/31 by Hiroya Nakao, Sho Yasui, Masashi Ota +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Control theory (sociology) #Dynamical systems theory #Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Oscillation (cell signaling) #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Phase (matter) #Phase synchronization #Physics #Quantum mechanics #Sensitivity (control systems) #Statistical physics #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.5009669
published as Chaos 28, 045103 (2018) · 10 pages, 5 figures, Revised version
openalex publication_date 2018/04/01 · arxiv created 2018/04/03 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.