Invariant curves in a discrete-time two-species system

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-09 DOI:10.1080/10236198.2023.2279632

Ryusuke Kon

{"title":"Invariant curves in a discrete-time two-species system","authors":"Ryusuke Kon","doi":"10.1080/10236198.2023.2279632","DOIUrl":null,"url":null,"abstract":"AbstractThe dynamics of discrete-time two-species systems may not be simple even if they have no positive fixed points. To reveal the behaviour of such systems, we focus on a special class of discrete-time two-species systems whose degenerate cases have a line segment of positive fixed points. As a main result, we show that the line segment of positive fixed points persists as an invariant curve under a small perturbation of the degenerate case. The absence of a positive fixed point ensures that such an invariant curve consists of heteroclinic orbits connecting two axial fixed points. The general result is applied to a discrete-time competition model of Ricker type with reproductive delay. The application reveals the existence of heteroclinic orbits connecting two axial 2-cycles, not only heteroclinic orbits connecting two axial fixed points.Keywords: Heteroclinic orbitinvariant curvecompetition systemRicker map2-cycleMathematic Subject classifications: 92-1092B0539A6039A3037N25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by JSPS KAKENHI Grant Number 20K03735, Japan.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2279632","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

AbstractThe dynamics of discrete-time two-species systems may not be simple even if they have no positive fixed points. To reveal the behaviour of such systems, we focus on a special class of discrete-time two-species systems whose degenerate cases have a line segment of positive fixed points. As a main result, we show that the line segment of positive fixed points persists as an invariant curve under a small perturbation of the degenerate case. The absence of a positive fixed point ensures that such an invariant curve consists of heteroclinic orbits connecting two axial fixed points. The general result is applied to a discrete-time competition model of Ricker type with reproductive delay. The application reveals the existence of heteroclinic orbits connecting two axial 2-cycles, not only heteroclinic orbits connecting two axial fixed points.Keywords: Heteroclinic orbitinvariant curvecompetition systemRicker map2-cycleMathematic Subject classifications: 92-1092B0539A6039A3037N25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by JSPS KAKENHI Grant Number 20K03735, Japan.

查看原文本刊更多论文

离散时间两种系统的不变曲线

摘要离散两种系统的动力学并不简单，即使它们没有正不动点。为了揭示这类系统的行为，我们研究了一类特殊的离散时间两种系统，它们的退化情况具有正不动点的线段。作为主要结果，我们证明了正不动点的线段在简并情形的小扰动下作为不变曲线存在。正不动点的不存在保证了这样的不变曲线由连接两个轴向不动点的异斜轨道组成。将一般结果应用于具有生殖延迟的Ricker型离散时间竞争模型。应用表明，不仅存在连接两个轴向不动点的异斜轨道，而且存在连接两个轴向不动点的异斜轨道。关键词:异斜轨道不变曲线竞争系统ricker map2-cycle数学学科分类:92-1092B0539A6039A3037N25披露声明作者未报告潜在利益冲突。本工作由日本JSPS KAKENHI基金号20K03735支持。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.