In this work we introduce and analyse a stochastic functional equation, which contains both delayed and advanced arguments. This equation results from adding a stochastic term to the discrete FitzHugh–Nagumo equation which arises in mathematical models of nerve conduction. A numerical method is introduced to compute approximate solutions and some numerical experiments are carried out to investigate their dynamical behaviour and compare them with the solutions of the corresponding deterministic equation.

CEMAT - Center for Computational and Stochastic Mathematics