{"title":"威布尔模型的动力学分析","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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
摘要
在这项工作中，我们研究了维度为一的 Weibull 模型的动力学，该模型由带三个参数的 Weibull 函数表示。我们研究了正定点，并用兰伯特 W 函数以及存在性和稳定性条件隐式地表达了这些定点。我们推断出，该 Weibull 函数定义了特定参数值下的阿利函数。为了说明理论结果，我们进行了数值模拟。
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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