What is Special Point

Self-regulating nonlinear waves in various biological populations are considered as moving attractors in excitable media. Mathematically, waves in populations are solutions of nonstationary parabolic systems of differential diffusion equations with source terms, and the velocity of the wave is an eigenvalue of the problem, and its profile is an eigenvalue function of the problem. There is no general exact method for solving such a problem. An approximate method for its solution is proposed (the semi-infinite reaction zone method), which essentially reduces to solving an algebraic system of equations. The method is used to calculate the waves in various biological populations. It is shown that there are two types of waves: a wave of conquest and a solitary wave. In all cases considered, formulas for calculating the velocity of the wave and its profile were obtained. One of the important examples considered is the analysis of solitary waves in populations of the herd locust.