Additive noise quenches delay-induced oscillations
1 Département de Neurosciences Fondamentales, University of Geneva, CMU - 1 Rue Michel Servet, 1211 Geneva 4, Switzerland
2 INRIA CR Nancy - Grand Est - 615 Rue du Jardin Botanique, 54602 Villers-les-Nancy Cedex, France, EU
Received: 14 March 2013
Accepted: 3 June 2013
Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interferes 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 a 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 delay-induced rhythmic solutions emerge.
PACS: 02.30.Ks – Delay and functional equations / 05.45.-a – Nonlinear dynamics and chaos / 02.50.Fz – Stochastic analysis
© EPLA, 2013