A numerical study of the optimal control problem for degenerate multicomponent mathematical model of the propagation of a nerve impulse in the system of nerves

The article is devoted to a numerical study of optimal regulation of propagation of a nerve impulse in the system of nerves, which can be constructed on the basis of the optimal control problem for degenerate FitzHugh–Nagumo system of equations. This model belongs to the class of reaction-diffusion models, which model a wide class of processes such as chemical reactions with diffusion and the propagation of a nerve impulse. In the case of asymptotic stability of the considered problem and under assumption that the rate of change of one component significantly exceeds the rate of the others, the model under study can be reduced to the optimal control problem for a semilinear Sobolev type equation with the initial Showalter–Sidorov condition. The article develops an algorithm for the numerical study of the model in the Maple environment. This algorithm is based on the Galerkin method and the decomposition method, which allows to take into account the phenomenon of degeneracy of the equation. The article gives an example illustrating the results of the computational experiment obtained by the two-component model on the two-ribbed graphs.