Additive noise quenches delay-induced oscillations

TL;DR

This paper demonstrates that additive noise can suppress delay-induced oscillations in nonlinear systems by shifting bifurcation thresholds, challenging previous assumptions about noise effects.

Contribution

It introduces a novel analysis showing additive noise influences the stability of delayed nonlinear systems using a time-dependent delayed center manifold reduction.

Findings

Additive noise shifts the bifurcation threshold for oscillations.

Noise intensity acts as a bifurcation parameter.

Delay-induced rhythmic solutions are affected by noise.

Abstract

Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We show this by performing a recently designed time-dependent delayed center manifold (DCM) reduction around an Hopf bifurcation in a model of nonlinear negative feedback. Using this, we show that noise intensity must be considered as a bifurcation parameter and thus shifts the threshold at which emerge delay-induced rhythmic solutions.