Delay stabilizes stochastic systems near a non-oscillatory instability
INRIA CR Nancy - Grand Est, Team CORTEX - 54600 Villers-les-Nancy, France, EU
2 Sprott Center - 501 Smyth Road, Ottawa, Ontario, Canada
3 Department of Physics, University of Ottawa - 50 Louis Pasteur, Ottawa, Ontario, K1N-6N5, Canada
Accepted: 26 March 2012
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 final 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.
PACS: 02.50.Fz – Stochastic analysis / 02.30.Ks – Delay and functional equations / 87.19.lc – Noise in the nervous system
© EPLA, 2012