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

S. V. Volkov

Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 575-595

Résumé

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.

Détail

Keywords: vector field, topological structure, critical point, separatrix, inverse problem of qualitative theory of ODE, mathematical model, programmed motion, controlled particle.
Mots-clés : ODE, phase portrait

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