Diverse routes to oscillation death in a coupled oscillator system

TL;DR

This paper provides exact analytical conditions for predicting oscillation death in coupled oscillators, revealing its dependence on multiple parameters and demonstrating robustness across different scenarios.

Contribution

It derives exact conditions for oscillation death via bifurcations in a well-known model, generalizing OD as sensitive to various parameters.

Findings

Oscillation death can be induced by changes in coupling, frequency, or amplitude.

Analytic conditions accurately predict bifurcation routes to OD.

Robustness of OD phenomena confirmed under noise and different oscillator counts.

Abstract

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory.