{"title":"Dynamics of a Lesile–Gower predator–prey model with square root response function and generalist predator","authors":"Mengxin He , Zhong Li","doi":"10.1016/j.aml.2024.109193","DOIUrl":null,"url":null,"abstract":"<div><p>A Leslie–Gower predator–prey model with square root response function and generalist predator is considered, and the existence and stability of equilibria of the system are discussed. It is shown that the system undergoes a degenerate Hopf bifurcation of codimension exactly two, where there exist two limit cycles. In addition, we find that the system has a cusp of codimension two and exhibits a Bogdanov–Takens bifurcation of codimension two. Our results reveal richer dynamics than the system with no generalist predator.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002131","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A Leslie–Gower predator–prey model with square root response function and generalist predator is considered, and the existence and stability of equilibria of the system are discussed. It is shown that the system undergoes a degenerate Hopf bifurcation of codimension exactly two, where there exist two limit cycles. In addition, we find that the system has a cusp of codimension two and exhibits a Bogdanov–Takens bifurcation of codimension two. Our results reveal richer dynamics than the system with no generalist predator.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.