{"title":"Comparison of solutions for non-monotone dynamical systems","authors":"Alain Rapaport , Oumaima Laraj , Noha El Khattabi","doi":"10.1016/j.sysconle.2024.105862","DOIUrl":null,"url":null,"abstract":"<div><p>We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke’s sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for the dynamics to preserve a partial order, which is not necessarily induced by a cone. Examples illustrate the results.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"191 ","pages":"Article 105862"},"PeriodicalIF":2.1000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124001506","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke’s sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for the dynamics to preserve a partial order, which is not necessarily induced by a cone. Examples illustrate the results.
期刊介绍：
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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