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

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 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.

arXiv comment10 pages, 5 figures, Revised version

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Cited by in corpus (10)

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• Entrainment of a network of interacting neurons with minimum stimulating charge
• The Winfree model with heterogeneous phase-response curves: Analytical results
• Phase-Amplitude Reduction and Optimal Phase Locking of Collectively Oscillating Networks
• Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
• Sparse optimization of mutual synchronization in collectively oscillating networks
• Extracting phase coupling functions between collectively oscillating networks directly from time-series data
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators