{"title":"Global bifurcation results for a delay differential system representing a chemostat model","authors":"Pablo Amster , Pierluigi Benevieri","doi":"10.1016/j.jde.2025.113222","DOIUrl":null,"url":null,"abstract":"<div><div>This paper studies a one-species chemostat model described by a system of differential delay equations, featuring a periodic input of a single nutrient with period <em>ω</em>. The delay represents the interval time between the consumption of the nutrient and its metabolization by the microbial species. We obtain global bifurcation results for the periodic solutions with period <em>ω</em>. Our proof is based on the application of the topological degree theory combined with a Whyburn-type Lemma.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113222"},"PeriodicalIF":2.4000,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625002256","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies a one-species chemostat model described by a system of differential delay equations, featuring a periodic input of a single nutrient with period ω. The delay represents the interval time between the consumption of the nutrient and its metabolization by the microbial species. We obtain global bifurcation results for the periodic solutions with period ω. Our proof is based on the application of the topological degree theory combined with a Whyburn-type Lemma.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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