# On a Fractional Stochastic Hodgkin-Huxley Model

## TL;DR

This paper introduces a stochastic Hodgkin-Huxley neuron model driven by fractional Brownian motion, incorporating rough path theory, and applies it to nerve fiber damage modeling.

## Contribution

It presents a novel fractional stochastic extension of the Hodgkin-Huxley model with viability conditions and demonstrates its application to nerve neuropathy.

## Key findings

- Model captures nerve damage effects on membrane potential
- Incorporates fractional Brownian motion for realistic noise modeling
- Provides a framework for future neurophysiological studies

## Abstract

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.