M. Hafdane, J. Collera, I. Agmour, Y. E. Foutayeni
{"title":"Hopf bifurcation for delayed prey-predator system with Allee effect","authors":"M. Hafdane, J. Collera, I. Agmour, Y. E. Foutayeni","doi":"10.28919/cmbn/7921","DOIUrl":null,"url":null,"abstract":". In this study, we take into account a predator-prey system with two delays, the prey is sea urchins and the predator is crabs. The focus is given to the Allee effect where the prey population undergoes, the poisoning of few predators, and a fishing effect on both species considered as selective for the prey. We aim to analyze the system’s stability around interior equilibrium using the theory of bifurcations and determine stability intervals related to delays. The theory of normal form and the center manifold are used to determine the direction of the bifurcations. Finally, numerical simulations are given by numerical methods in DDE-Biftool Matlab package to illustrate the theoretical results.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Biology and Neuroscience","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28919/cmbn/7921","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 1
Abstract
. In this study, we take into account a predator-prey system with two delays, the prey is sea urchins and the predator is crabs. The focus is given to the Allee effect where the prey population undergoes, the poisoning of few predators, and a fishing effect on both species considered as selective for the prey. We aim to analyze the system’s stability around interior equilibrium using the theory of bifurcations and determine stability intervals related to delays. The theory of normal form and the center manifold are used to determine the direction of the bifurcations. Finally, numerical simulations are given by numerical methods in DDE-Biftool Matlab package to illustrate the theoretical results.
期刊介绍:
Communications in Mathematical Biology and Neuroscience (CMBN) is a peer-reviewed open access international journal, which is aimed to provide a publication forum for important research in all aspects of mathematical biology and neuroscience. This journal will accept high quality articles containing original research results and survey articles of exceptional merit.