Impact of symmetry breaking in networks of globally coupled oscillators

TL;DR

This paper investigates how breaking symmetry in globally coupled oscillator networks leads to increased dynamical complexity, revealing new states and transition routes, supported by analytical and numerical analysis.

Contribution

It introduces the effects of symmetry breaking on dynamical states in coupled oscillators, identifying new states and transition pathways not seen in symmetric cases.

Findings

Symmetry breaking induces amplitude and frequency chimeras and clusters.

Disparate routes to chimera death are observed with symmetry breaking.

Analytical verification of chimera death regions supports numerical results.

Abstract

We analyze the consequences of symmetry breaking in the coupling in a network of globally coupled identical Stuart-Landau oscillators. We observe that symmetry breaking leads to increased disorderliness in the dynamical behavior of oscillatory states and consequently results in a rich variety of dynamical states. Depending on the strength of the nonisochronicity parameter, we find various dynamical states such as amplitude chimera, amplitude cluster, frequency chimera and frequency cluster states. In addition we also find disparate transition routes to recently observed chimera death state in the presence of symmetry breaking even with global coupling. We also analytically verify the chimera death region which corroborates the numerical results. The above results are compared with that of the symmetry preserving case as well.