Stochastic center manifold analysis in scalar nonlinear systems involving distributed delays and additive noise

Axel Hutt 1 Jérémie Lefebvre 2
1 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 : This study reviews and extends a recent center manifold analysis technique developped to characterize stochastic bifurcations in delayed systems induced by additive noise. Motivated by the dynamics of spatially extended neural field models with finite propagation velocity, we revealed and fully characterized codimension 1 stochastic bifurcations induced by additive white noise. In contrast to previous studies, we here extended our analysis to the case of distributed delays while applying our results to the stochastic Hopf bifurcation. Taken together, our results provide further insight on the conjugate role of noise and delays in the genesis non-linear phenomena.
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Axel Hutt, Jérémie Lefebvre. Stochastic center manifold analysis in scalar nonlinear systems involving distributed delays and additive noise. Markov Processes and Related Fields, Polymath, 2014, in press. ⟨hal-01006388v2⟩

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