Numerical Simulation of Neural Fields with Finite Transmission Speed and Random Disturbance

This paper aims at presenting an efficient and accurate numerical method for treating both deterministic and stochastic Neural Field Equations(NFEs) with a finite signal transmission speed and in the presence of external stimuli input. The numerical integration tool devised belongs to the class of Galerkin-type spectral approximations, and our particular effort focuses on an efficient implementation of the solution technique because of the partial integro-differential fashion of the NFEs in use. This method is intended for implementation in MATLAB. Its performance and efficiency is investigated on an NFE model with external stimuli inputs. We study both the deterministic case of the mentioned model and its stochastic counterpart to observe important differences in the solution behavior when the assumption of finite/infinite transmission speed implemented.