Additive noise quenches delay-induced oscillations

Jérémie Lefebvre 1 Axel Hutt 2
2 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
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 sys- tems 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 bifur- cation parameter and thus shifts the threshold at which emerge delay-induced rhythmic solutions.
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Jérémie Lefebvre, Axel Hutt. Additive noise quenches delay-induced oscillations. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2013, ⟨10.1209/0295-5075/102/60003⟩. ⟨hal-00847167⟩

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