混合单调性 k 维离散系统中的吸引子

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-20 DOI:10.1007/s12346-024-01123-8
Ziyad AlSharawi, Jose S. Cánovas, Sadok Kallel
{"title":"混合单调性 k 维离散系统中的吸引子","authors":"Ziyad AlSharawi, Jose S. Cánovas, Sadok Kallel","doi":"10.1007/s12346-024-01123-8","DOIUrl":null,"url":null,"abstract":"<p>We consider <i>k</i>-dimensional discrete-time systems of the form <span>\\(x_{n+1}=F(x_n,\\ldots ,x_{n-k+1})\\)</span> in which the map <i>F</i> is continuous and monotonic in each one of its arguments. We define a partial order on <span>\\({\\mathbb {R}}^{2k}_+\\)</span>, compatible with the monotonicity of <i>F</i>, and then use it to embed the <i>k</i>-dimensional system into a 2<i>k</i>-dimensional system that is monotonic with respect to this poset structure. An analogous construction is given for periodic systems. Using the characteristics of the higher-dimensional monotonic system, global stability results are obtained for the original system. Our results apply to a large class of difference equations that are pertinent in a variety of contexts. As an application of the developed theory, we provide two examples that cover a wide class of difference equations, and in a subsequent paper, we provide additional applications of general interest.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Attractors in k-Dimensional Discrete Systems of Mixed Monotonicity\",\"authors\":\"Ziyad AlSharawi, Jose S. Cánovas, Sadok Kallel\",\"doi\":\"10.1007/s12346-024-01123-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider <i>k</i>-dimensional discrete-time systems of the form <span>\\\\(x_{n+1}=F(x_n,\\\\ldots ,x_{n-k+1})\\\\)</span> in which the map <i>F</i> is continuous and monotonic in each one of its arguments. We define a partial order on <span>\\\\({\\\\mathbb {R}}^{2k}_+\\\\)</span>, compatible with the monotonicity of <i>F</i>, and then use it to embed the <i>k</i>-dimensional system into a 2<i>k</i>-dimensional system that is monotonic with respect to this poset structure. An analogous construction is given for periodic systems. Using the characteristics of the higher-dimensional monotonic system, global stability results are obtained for the original system. Our results apply to a large class of difference equations that are pertinent in a variety of contexts. As an application of the developed theory, we provide two examples that cover a wide class of difference equations, and in a subsequent paper, we provide additional applications of general interest.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12346-024-01123-8\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01123-8","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

摘要

我们考虑形式为 \(x_{n+1}=F(x_n,\ldots ,x_{n-k+1})\ 的 k 维离散时间系统,其中映射 F 在其每个参数中都是连续且单调的。我们在 \({\mathbb {R}}^{2k}_+\) 上定义了一个与 F 的单调性兼容的偏序,然后用它把 k 维系统嵌入到一个 2k 维系统中,这个 2k 维系统相对于这个正集结构是单调的。对于周期系统,我们也给出了类似的构造。利用高维单调系统的特征,可以得到原始系统的全局稳定性结果。我们的结果适用于一大类与各种情况相关的差分方程。作为所开发理论的应用,我们提供了两个涵盖各类差分方程的示例,并在后续论文中提供了更多具有普遍意义的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Attractors in k-Dimensional Discrete Systems of Mixed Monotonicity

We consider k-dimensional discrete-time systems of the form \(x_{n+1}=F(x_n,\ldots ,x_{n-k+1})\) in which the map F is continuous and monotonic in each one of its arguments. We define a partial order on \({\mathbb {R}}^{2k}_+\), compatible with the monotonicity of F, and then use it to embed the k-dimensional system into a 2k-dimensional system that is monotonic with respect to this poset structure. An analogous construction is given for periodic systems. Using the characteristics of the higher-dimensional monotonic system, global stability results are obtained for the original system. Our results apply to a large class of difference equations that are pertinent in a variety of contexts. As an application of the developed theory, we provide two examples that cover a wide class of difference equations, and in a subsequent paper, we provide additional applications of general interest.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Accounts of Chemical Research
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.
期刊最新文献
Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1