LAUSR

The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of a nerve impulse in a membrane. The model consists of an integro-differential equation with initial conditions (the Cauchy problem). The difference kernel (memory function) of the model equation was chosen as a power function so that it can be rewritten in terms of the fractional derivative. For the Cauchy problem, an explicit finite-difference scheme is constructed, and an investigation of its stability and convergence was performed in computer experiments. The finite-difference scheme was implemented in the Maple computer program, with the help of which the simulation results were visualized, and oscillograms and phase trajectories were obtained.