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Journal Articles EPL - Europhysics Letters Year : 2012

Delay stabilizes stochastic systems near an non-oscillatory instability

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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Dates and versions

hal-00710426 , version 1 (20-06-2012)

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Axel Hutt, Jérémie Lefebvre, André Longtin. Delay stabilizes stochastic systems near an non-oscillatory instability. EPL - Europhysics Letters, 2012, 98 (2), pp.200004. ⟨10.1209/0295-5075/98/20004⟩. ⟨hal-00710426⟩
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