Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators

TL;DR

This paper uncovers a novel symmetry-breaking transition in coupled oscillators caused by local filtering, shifting from homogeneous to inhomogeneous limit cycles, supported by bifurcation analysis and experimental validation.

Contribution

It introduces the first detailed analysis of a symmetry-breaking transition induced by local filtering in coupled oscillators, combining theoretical and experimental approaches.

Findings

Transition occurs in the parametric zone of rhythmogenesis and oscillation death.

The transition is robust against parameter fluctuations and noise.

Bifurcation analysis explains the transition mechanism.

Abstract

We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise.