{"title":"Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs","authors":"M. Hafdane, I. Agmour, Y. El Foutayeni","doi":"10.23939/mmc2023.01.066","DOIUrl":null,"url":null,"abstract":"In this paper, we have a discrete delayed dynamic system of three marine species: prey, predator, and superpredator. In addition to the effect of prey toxicity, we consider the negative fishing effect of these species. The study of this model consists of the search for equilibria with eigenvalue analysis, the existence of Hopf bifurcations at interior equilibria, and the determination of direction and stability analysis of Hopf bifurcation using the theory of normal form and center manifold. Some examples are given with numerical simulations to illustrate the results in different cases of delay.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modeling and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/mmc2023.01.066","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we have a discrete delayed dynamic system of three marine species: prey, predator, and superpredator. In addition to the effect of prey toxicity, we consider the negative fishing effect of these species. The study of this model consists of the search for equilibria with eigenvalue analysis, the existence of Hopf bifurcations at interior equilibria, and the determination of direction and stability analysis of Hopf bifurcation using the theory of normal form and center manifold. Some examples are given with numerical simulations to illustrate the results in different cases of delay.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
