{"title":"具有恐惧效应和多重延迟的改良莱斯利-高尔捕食者-猎物模型的分岔分析","authors":"Shuo Yao, Jingen Yang, Sanling Yuan","doi":"10.3934/mbe.2024249","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays.\",\"authors\":\"Shuo Yao, Jingen Yang, Sanling Yuan\",\"doi\":\"10.3934/mbe.2024249\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.</p>\",\"PeriodicalId\":49870,\"journal\":{\"name\":\"Mathematical Biosciences and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Biosciences and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3934/mbe.2024249\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mbe.2024249","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays.
In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.
期刊介绍:
Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing.
MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).