A Polynomial System of Degree Four with an Invariant Square Containing At Least Five Limit Cycles

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-26 DOI:10.1007/s12346-024-01106-9

Maite Grau, Iván Szántó

引用次数: 0

Abstract

We consider a class of polynomial systems of degree four with four real invariant straight lines that form a square, called this an invariant square, and also that contains in its interior at least five small amplitude limit cycles for a certain choice of the parameters. Moreover, we will obtain the necessary and sufficient conditions for the critical point inside the square to be a center.

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度数为四的多项式系统，其不变平方至少包含五个极限循环

我们考虑一类具有四条实不变直线的四度多项式系统，这些直线构成一个正方形，称为不变正方形，并且在其内部包含至少五个小振幅极限循环（参数选择一定）。此外，我们还将获得正方形内部临界点成为中心的必要条件和充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.