Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh–Nagumo equation

• We have analysed a stochastic functional equation, which contains both delayed and advanced arguments.
• We have created a new computational algorithm to approximate this equation, based on the Euler–Maruyama method.
• We have analysed noise induced changes in the dynamical behaviour of equations.
• We observe that a low level of noise is enough to produce a significantly different dynamical behaviour of the solutions.
• We further observe that the effect of noise is much stronger in the region where the solutions change faster.

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.