Synchronization of multi-phase oscillators: An Axelrod-inspired model

Abstract

Inspired by Axelrod's model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction --which occurs between homologous phases-- is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where some of the phases of a given oscillator can be synchronized to a certain cluster, while its other phases are synchronized to different clusters.