Numerical Evaluations for Fractional Stochastic Differential Equations in Neuronal Dynamics

We consider two coupled fractional stochastic differential equations useful to model activity of the neuronal membrane voltage subject to a correlated input. We give the explicit expression of the solution processes. In particular, we develop the calculation of the covariance of the neuronal process and we provide numerical evaluations for different values of specified parameters. We show that the different time-scales adopted for the involved dynamics and the correlation in the input process affect the behavior of the covariance of the resulting process. In this sense, the proposed model is able to preserve memory effects.