广义Liénard系统极限环的唯一性

IF 1 4区 数学 Q1 MATHEMATICS
HuiPing Zhou, Yueding Yuan
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引用次数: 0

摘要

摘要在这篇文章中,一般的Liénard系统d x d t=ξ(y)−F(x),d y d t=−g(x)\left\{\begin{array}{l}\frac{\rm{d}}x}。进行了研究。利用Filippov变换,结合对闭合轨道发散的仔细估计,我们证明了该系统极限环唯一性的充分条件。我们的结果扩展了几乎所有现有的关于Liénard系统的相关研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the uniqueness of limit cycles for generalized Liénard systems
Abstract In this article, the general Liénard system d x d t = ϕ ( y ) − F ( x ) , d y d t = − g ( x ) \left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system.
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来源期刊
Open Mathematics
Open Mathematics MATHEMATICS-
CiteScore
2.40
自引率
5.90%
发文量
67
审稿时长
16 weeks
期刊介绍: Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
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