Construction of Flat Vector Fields with Prescribed Global Topological Structures

In this paper, we present a method for constructing vector fields whose phase portraits have finite sets of prescribed special trajectories (limit cycles, simple and complex singular points, separatrices) and prescribed topological structures in limited domains of the phase plane. The problem of constructing such vector fields is a generalization of a number of well-known inverse problems of the qualitative theory of ordinary differential equations. The proposed method for solving it expands the possibilities of mathematical modeling of dynamic systems with prescribed properties in various fields of science and technology.