Mathematical Model of the Hereditary FitzHugh–Nagumo Oscillator

In this paper, we propose a new mathematical FitzHugh–Nagumo model with memory, which describes the propagation of nerve impulses in membranes. This model is an integro-differential equation with initial conditions (the Cauchy problem). The difference kernel (memory function) of the model equation is a power function; this allows one to rewrite it in terms of fractional derivatives. For the Cauchy problem, an explicit finite-difference scheme was constructed and examined by computer experiments on stability and convergence. The finite-difference scheme was implemented in the Maple software; simulation results were visualized, oscillograms and phase trajectories were obtained.