Modelling and analysis of spatially extended stochastic FitzHugh-Nagumo systems
Spatially extended neural systems subject to noise can be rigorously modelled as stochastic evolution systems driven by function-valued stochastic processes, e.g. Wiener or Levy noise. In this talk, we demonstrate how to use this approach to analyze and quantify stochastic perturbations to the propagation of the action potential along the axon of a single neuron in the FitzHugh-Nagumo model. Using a novel approach via functional inequalities we study various properties of the action potential in terms of the covariance structure of the driving stochastic forcing terms.