Construction of the planar vector fields with nonsimple critical point of prescribed topological structure

The problem of constructing $n$-linear ($n\geq 2$) plane vector fields with isolated critical point and given separatrices of prescribed types is considered. Such constructions are based on the use of vector algebra, the qualitative theory of second-order dynamic systems and classical methods for investigating their critical points. This problem is essentially an inverse problem of the qualitative theory of ordinary differential equations, and its solution can be used to synthesize mathematical models of controlled dynamical systems of various physical nature.