Delay stabilizes stochastic systems near an non-oscillatory instability

Axel Hutt 1 Jérémie Lefebvre 2 André Longtin 2
1 CORTEX - Neuromimetic intelligence
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : The work discovers a stochastic bifurcation in delayed systems in the presence of both delay and additive noise. To understand this phenomenon we present a stochastic center manifold method to compute a non-delayed stochastic order parameter equation for a scalar delayed system driven by additive uncorrelated noise. The derived order parameter equation includes additive and multiplicative white and coloured noise. An illustrative neural system with delayed self-excitation reveals stationary states that are postponed by combined additive noise and delay. A nal brief analytical treatment of the derived order parameter equation reveals analytically the shift of the stationary states which depends on the delay and the noise strength.
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Axel Hutt, Jérémie Lefebvre, André Longtin. Delay stabilizes stochastic systems near an non-oscillatory instability. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2012, 98, pp.200004. ⟨hal-00710426⟩

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