Construction of Planar Vector Fields with a Nonsimple Critical Point of Prescribed Topological Structure

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 283; no. 1; pp. 20 - 39
• Main Author: Volkov, S. V.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2024; Springer Nature B.V
• Subjects: Critical point; Differential equations; Dynamical systems; Fields (mathematics); Inverse problems; Mathematics; Mathematics and Statistics; controlled particle; ODE; critical point; topological structure; vector field; mathematical model; separatrix; programmed motion; inverse problem of qualitative theory of ODE; phase portrait
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-024-07237-3

The problem of constructing
n
-linear (
n ≥
2) plane vector fields with an 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.