Analysis of the approximate differential equation in one-dimensional model of the brain cortex dynamics

An ordinary differential equation of second order is considered as a model of a stationary process of the of the cerebral cortex activation. Two types of approximations of the non lineal member of this equation are used and compared: 1) sigmoid function of the exponential type; 2) new type of approximation as a lineal spline. Algorithms for the solution of the direct initial problem, corresponding to each of the approximations, are constructed and carried out as computing programs in the MatLab system. The quality of two approximations is compared on the numerical experiments for synthetic examples.