Symmetry breaking induced tipping to aging

TL;DR

This paper investigates how heterogeneity and symmetry-breaking coupling induce transitions in globally coupled Stuart-Landau oscillators, revealing bifurcation-induced tipping to an aging state and analyzing stability through mean-field bifurcation diagrams.

Contribution

It introduces a mean-field approach to analyze bifurcations in coupled oscillators, elucidating the mechanisms behind symmetry-breaking induced aging transitions.

Findings

Heterogeneity favors oscillatory states at low symmetry-breaking coupling.

Transition to an aging state occurs via Hopf and pitchfork bifurcations.

Analytical bifurcation curves agree with simulation results.

Abstract

The competing effect of heterogeneity and symmetry breaking coupling on the emerging dynamics in a system of N globally coupled Stuart-Landau oscillators is investigated. Increasing the heterogeneity, using the standard deviation of the Hopf bifurcation parameter, favors the macroscopic oscillatory state for low values of the symmetry breaking coupling and inhomogeneous steady state for larger values of the coupling. There is also a transition, tipping, to homogeneous steady state (aging state) from the macroscopic oscillatory state. The limiting factor in the diffusive coupling favors the macroscopic oscillatory state even in the presence of a large fraction of inactive oscillators in the network thereby increasing the robustness of the network. The globally coupled oscillators are reduced to a system of two evolution equations for the macroscopic order parameters, corresponding to the mean-field and the shape parameter, using the self-consistent field approach. The bifurcation diagrams obtained from the mean-field variables elucidate various bifurcation scenarios responsible for the dynamical transitions observed in N globally coupled Stuart-Landau oscillators. In particular, tipping to the aging state is found to occur via the Hopf and pitchfork bifurcations illustrating the phenomenon of bifurcation induced tipping. Analytical stability (critical) curves of these bifurcations, deduced from the mean-field variables, are found to fairly well agree with the simulation results.