Stable and transient multi-cluster oscillation death in nonlocally coupled networks

TL;DR

This paper investigates multi-cluster oscillation death in nonlocally coupled Stuart-Landau oscillators, revealing stable and transient behaviors influenced by coupling parameters, with analytical predictions matching numerical simulations.

Contribution

It introduces an analytical framework beyond mean-field theory to predict stability boundaries and transient times in multi-cluster oscillation death.

Findings

Stable multi-cluster oscillation death patterns identified.

Transient regimes approaching synchronized oscillations observed.

Analytical predictions align with numerical results for various coupling ranges.

Abstract

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation which works well for large coupling ranges but fails for coupling ranges which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.