Stochastic model for signal propagation

A key for understanding any information process depends on the nature of the signal propagation. This article introduces a one-dimensional model that describes the passage of the signal through a duct. The Fokker–Planck equation, a stochastic equation, is used, and a drive force function is suggested to model the behavior of the signal transmission. Solving the Fokker–Planck equation for the equilibrium state, we find the solvable potential of an analytical system and obtain the exact probability density function, which is used to obtain a characteristic time for the passage of information. This kind of model can be used for a lot of different problems. As an application, we try to understand the ionic firing in axons. The parameters introduced in the model are fixed from phenomenological data related to a human femoral motor neuron.