{"title":"Dynamics analysis of the Weibull model","authors":"Chabane Bedjguelel, Hacene Gharout, Bakir Farhi","doi":"10.24193/mathcluj.2023.2.04","DOIUrl":null,"url":null,"abstract":"In this work, we study the dynamics of the Weibull model in dimension one, represented by the Weibull function with three parameters. The positive fixed points have been studied and implicitly expressed in terms of the Lambert W-function as well as the existence and stability conditions. We deduce that this Weibull function defines an Allee function for certain parameter values. Numerical simulations have been presented to illustrate the theoretical results.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":"74 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2023.2.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we study the dynamics of the Weibull model in dimension one, represented by the Weibull function with three parameters. The positive fixed points have been studied and implicitly expressed in terms of the Lambert W-function as well as the existence and stability conditions. We deduce that this Weibull function defines an Allee function for certain parameter values. Numerical simulations have been presented to illustrate the theoretical results.
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