Construction of domains of attraction at degeneration of singularly perturbed equations

The paper presents the analysis of singularly perturbed systems of ordinary differential equations. The overview of known results on the considered issue is given and the degree of relevance of the problem under investigation is substantiated based on them. We consider a system of singularly perturbed ordinary differential equations with analytic functions in the complex domain. A degenerate system corresponding to the system under consideration loses its uniqueness under degeneracy. In order to analyze the solution of the initial problem with respect to a small parameter, we introduce the notion of the domain of attraction of a solution of a degenerate system. The problem is reduced to finding the domains of attraction. Domains are constructed with the use of the level line of harmonic functions in the complex domain, and it is proved that they are domains of attraction of the solutions of the degenerate system under consideration.