{"title":"A note on Monotone Systems with Positive Translation Invariance","authors":"D. Angeli, E. Sontag","doi":"10.1109/MED.2006.328782","DOIUrl":null,"url":null,"abstract":"We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration","PeriodicalId":347035,"journal":{"name":"2006 14th Mediterranean Conference on Control and Automation","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 14th Mediterranean Conference on Control and Automation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MED.2006.328782","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration
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