GEOMETRIC THEORY OF A SINGULARLY PERTURBED BERNULLI EQUATION WITH A PASS POINT

Abstract

In this article, we consider a singularly perturbed equation with a saddle point. The definitions of boundary-layer lines, boundary-layer regions, and areas of attraction from early works are given. According to the adopted definitions, the task was set to study the regions of attraction, boundary layer regions and lines, regular and singular regions, and to note significant differences. By applying a conformal transformation, the problem is reduced to a standard form, geometric constructions of regions are carried out using the line of levels of harmonic functions. All constructions are accompanied by corresponding figures. In the future, the results of this work can be used for the theory of singularly perturbed equations in the complex domain. The results obtained can be used to study phenomena that can be in various stationary states. The discovered new boundary-layer lines and regions take place for equations of a more general form.