Some Fractional Stochastic Models for Neuronal Activity with Different Time-Scales and Correlated Inputs

Abstract

In order to describe neuronal dynamics on different time-scales, we propose a stochastic model based on two coupled fractional stochastic differential equations, with different fractional orders. For the specified choice of involved functions and parameters, we provide three specific models, with/without leakage, with fractional/non-fractional correlated inputs. We give explicit expressions of the process representing the voltage variation in the neuronal membrane. Expectation values and covariances are given and compared. Numerical evaluations of the average behaviors of involved processes are presented and discussed.

Keywords

• fractional stochastic differential equations
• neuronal models
• correlation