Document Type
Article
Department
Mathematics
Publication Date
2019
Abstract
With the recent development of analytical methods for studying the collective dynamics of coupled oscillator systems, the dynamics of communities of coupled oscillators have received a great deal of attention in the nonlinear dynamics community. However, the majority of these works treat systems with a number of symmetries to simplify the analysis. In this work we study the role of symmetry and symmetry-breaking in the collective dynamics of coupled oscillator communities, allowing for a comparison between the macroscopic dynamics of symmetric and asymmetric systems. We begin by treating the symmetric case, deriving the bifurcation diagram as a function of intra- and intercommunity coupling strengths. In particular we describe transitions between incoherence, standing wave, and partially synchronized states and reveal bistability regions. When we turn our attention to the asymmetric case we find that the symmetry-breaking complicates the bifurcation diagram. For instance, a pitchfork bifurcation in the symmetric case is broken, giving rise to a Hopf bifurcation. Moreover, an additional partially synchronized state emerges, as well as a new bistability region.
Publication Title
The European Physical Journal B
Volume
92
First Page
46
DOI
10.1140/epjb/e2019-90543-x
Comments
Author's accepted manuscript provided by the Trinity College Digital Repository in accordance with the publisher's policies. Published version available as:
Per Sebastian Skardal. “Symmetry and Symmetry Breaking in Coupled Oscillator Communities.” The European Physical Journal B 92 (2019): 46.
https://doi.org/10.1140/epjb/e2019-90543-x