Numerical Simulations of SDEs and SPDEs From Neural Systems Using SDELab

Stochastic differential equations are an important class of models that allow for a time varying random forcing in standard deterministic differential equations. We introduce the Itô stochastic differential equation as a generalisation of the standard finite dimensional initial value problem for ODEs. The Hodgkin-Huxley model is given as an example. We also look at reaction-diffusion equations, in particular the FitzHugh-Nagumo model, under the influence of stochastic forcing. Examples are given in the computer environment MATLAB.