{"title":"具有两个延迟和选择性收获的捕食-捕食系统的Hopf分岔","authors":"Feng-mei Zhang, Wencheng Chen, Peng Liu","doi":"10.1117/12.2679278","DOIUrl":null,"url":null,"abstract":"In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hopf bifurcation of a prey-predator system with two delays and selective harvesting\",\"authors\":\"Feng-mei Zhang, Wencheng Chen, Peng Liu\",\"doi\":\"10.1117/12.2679278\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.\",\"PeriodicalId\":301595,\"journal\":{\"name\":\"Conference on Pure, Applied, and Computational Mathematics\",\"volume\":\"63 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Conference on Pure, Applied, and Computational Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1117/12.2679278\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Conference on Pure, Applied, and Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1117/12.2679278","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hopf bifurcation of a prey-predator system with two delays and selective harvesting
In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.
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