Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization

Abstract

A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensemble synchronization. Following a short report of our preliminary results [Phys. Rev. E. {\bf 78}, 025201(R) (2008)], we present a more detailed study of the effects of coupling, noise and phase asymmetries in coupled phase oscillator ensembles. We identify five distinct synchronization regions, and new routes to synchronization that are characteristic of the coupling asymmetry. We show that noise asymmetry induces effects similar to that of coupling asymmetry when the latter is absent. We also find that phase asymmetry controls the probability of occurrence of particular routes to synchronization. Our results suggest that asymmetry plays a crucial role in controlling synchronization within and between oscillator ensembles, and hence that its consideration is vital for modeling real life problems.

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• Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
• Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
• Phase synchronization between collective rhythms of fully locked oscillator groups
• Sparse optimization of mutual synchronization in collectively oscillating networks
• Two-community noisy Kuramoto model with general interaction strengths: Part I
• Metastability of multi-population Kuramoto-Sakaguchi oscillators