{"title":"Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response","authors":"Wahiba Khellaf, N. Hamri","doi":"10.1155/2010/813289","DOIUrl":null,"url":null,"abstract":"We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2010 1","pages":"1-24"},"PeriodicalIF":0.0000,"publicationDate":"2010-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2010/813289","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Nonlinear Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2010/813289","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.
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