Title: 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.