On Limit Cycles of Autonomous Systems

Авторы: Ivanova T.M., Kostin A.B., Rubinshtein A.I., Sherstyukov V.B.
Журнал: Journal of Mathematical Sciences
Том: 286
Номер: 1
Год издания: 2024
Издательство: Plenum Publishers
Местоположение издательства: United States
Первая страница: 68
Последняя страница: 88
DOI: 10.1007/s10958-024-07491-5
Аннотация: We consider the problem of the existence of limit cycles for autonomous systems of differentialequations. We present quite elementary considerations that can be useful in discussing qualitativeissues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation F(x, y) = 1 with a sufficiently general function F is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems dependingon the real parameter). These systems are written out explicitly. We analyze in detail several specificexamples. Graphic illustrations are provided.
Добавил в систему: Шерстюков Владимир Борисович

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