Noise-driven bifurcations in a nonlinear Fokker–Planck system describing stochastic neural fields

Pulse Bifurcations in Stochastic Neural Fields

We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integral term characterizing synaptic interactions between neurons at different spatial locations of the network. We introduce an auxiliary variable to model the effects of local negative feedback and consider random fluctu...

Nonlinear Langevin Equations for Wandering Patterns in Stochastic Neural Fields

We analyze the effects of additive, spatially extended noise on spatiotemporal patterns in continuum neural fields. Our main focus is how fluctuations impact patterns when they are weakly coupled to an external stimulus or another equivalent pattern. Showing the generality of our approach, we study both propagating fronts and stationary bumps. Using a separation of time scales, we represent the...

Stochastic PDE's driven by Nonlinear Noise and Backward Doubly SDE's

Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model

The stochastically forced three-dimensional Hindmarsh–Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits monoand bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, ...

Stochastic Sensitivity and Noise-Induced Bifurcations of Limit Cycles

Introduction Analysis of the forced nonlinear dynamical systems plays an important role for understanding of the various noise-induced phenomena in mechanics, electronics, biology and economics. Even small random disturbances may essentially change behavior of the dynamic system and generate noise-induced transitions, stochastic bifurcations, noise-induced order and chaos [1-7]. In the present ...