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

TL;DR

This paper investigates how asymmetries in coupling, noise, and phase affect synchronization routes in coupled oscillator ensembles, revealing new pathways and emphasizing the importance of asymmetry in modeling real systems.

Contribution

It provides a detailed analysis of asymmetry effects on synchronization routes, identifying five distinct regions and the influence of different asymmetries, which was not previously explored in depth.

Findings

Five distinct synchronization regions identified.

Noise asymmetry mimics coupling asymmetry effects.

Phase asymmetry influences route probabilities.

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.