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

被引：0
作者：
Volkov S.V. [1 ]
机构：
[1] RUDN University, Moscow
来源：
Journal of Mathematical Sciences | 2024年 / 283卷 / 1期
关键词：
controlled particle; critical point; inverse problem of qualitative theory of ODE; mathematical model; ODE; phase portrait; programmed motion; separatrix; topological structure; vector field;
D O I：
10.1007/s10958-024-07237-3
中图分类号：
学科分类号：
摘要：
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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
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页码：20 / 39
页数：19
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