Phase resetting, clusters, and waves in a lattice of coupled oscillatory units

Abstract

A one-dimensional chain consisting of many locally coupled oscillatory units is considered when both diffusive (linear) and nonlinear interactions exist. The dynamics of units may also be altered by a weak white Gaussian noise. Two different collective evolutionary paths have been identified in the chain: (i) the onset of temporal phase clusters and their subsequent breakdown or reconstruction through phase resetting, and (ii) the formation of a phase wave during a process of selforganization. Such a wave may originate from an initially disordered pattern after appropriate reorganization of phases and amplitudes occurring on a time lapse that can be very long.