Symmetry and symmetry breaking in coupled oscillator communities

Per Sebastian Skardal ()
Additional contact information
Per Sebastian Skardal: Trinity College

The European Physical Journal B: Condensed Matter and Complex Systems, 2019, vol. 92, issue 2, 1-11

Abstract: 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 inter-community 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. Graphical abstract

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/e2019-90543-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:92:y:2019:i:2:d:10.1140_epjb_e2019-90543-x

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2019-90543-x

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().