Alon Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, Eduardo Sontag
{"title":"反应网络的契约性与单调性之间的相互作用","authors":"Alon Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, Eduardo Sontag","doi":"arxiv-2404.18734","DOIUrl":null,"url":null,"abstract":"This work studies relationships between monotonicity and contractivity, and\napplies the results to establish that many reaction networks are weakly\ncontractive, and thus, under appropriate compactness conditions, globally\nconvergent to equilibria. Verification of these properties is achieved through\na novel algorithm that can be used to generate cones for monotone systems. The\nresults given here allow a unified proof of global convergence for several\nclasses of networks that had been previously studied in the literature.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interplay between Contractivity and Monotonicity for Reaction Networks\",\"authors\":\"Alon Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, Eduardo Sontag\",\"doi\":\"arxiv-2404.18734\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work studies relationships between monotonicity and contractivity, and\\napplies the results to establish that many reaction networks are weakly\\ncontractive, and thus, under appropriate compactness conditions, globally\\nconvergent to equilibria. Verification of these properties is achieved through\\na novel algorithm that can be used to generate cones for monotone systems. The\\nresults given here allow a unified proof of global convergence for several\\nclasses of networks that had been previously studied in the literature.\",\"PeriodicalId\":501325,\"journal\":{\"name\":\"arXiv - QuanBio - Molecular Networks\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuanBio - Molecular Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2404.18734\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuanBio - Molecular Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.18734","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interplay between Contractivity and Monotonicity for Reaction Networks
This work studies relationships between monotonicity and contractivity, and
applies the results to establish that many reaction networks are weakly
contractive, and thus, under appropriate compactness conditions, globally
convergent to equilibria. Verification of these properties is achieved through
a novel algorithm that can be used to generate cones for monotone systems. The
results given here allow a unified proof of global convergence for several
classes of networks that had been previously studied in the literature.