The discontinuous planar piecewise linear systems with two improper nodes have at most one limit cycle

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.1016/j.nonrwa.2024.104180

Lu Chen, Changjian Liu

引用次数: 0

Abstract

The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincaré half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.

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有两个不恰当节点的不连续平面片断线性系统最多有一个极限周期

我们研究了具有两个不适当节点的平面片断线性系统的极限循环的存在性和数量。通过构造波恩卡半映射和后继函数，我们证明了这类系统最多只有一个极限循环，而且当极限循环存在时，它一定是双曲的。此外，我们明确给出了极限循环存在的参数区域。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.