On a Multifractional Stochastic Hodgkin-Huxley Model

The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for $\mathbb R\times [0,1]^3$. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.