{"title":"Hopf bifurcation for a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge","authors":"Tongtong Chen, Jixun Chu","doi":"10.3934/dcdsb.2022082","DOIUrl":null,"url":null,"abstract":"In this paper, a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge is investigated. The model is formulated as an abstract non-densely defined Cauchy problem and a sufficient condition for the existence of the positive age-related equilibrium is given. Then using the integral semigroup theory and the Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that Hopf bifurcation occurs at the positive age-related equilibrium. Numerical simulations are performed to validate theoretical results and sensitivity analyses are presented. The results show that the prey refuge has a stabilizing effect, that is, the prey refuge is an important factor to maintain the balance between prey and predator population.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"43 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series B","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcdsb.2022082","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge is investigated. The model is formulated as an abstract non-densely defined Cauchy problem and a sufficient condition for the existence of the positive age-related equilibrium is given. Then using the integral semigroup theory and the Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that Hopf bifurcation occurs at the positive age-related equilibrium. Numerical simulations are performed to validate theoretical results and sensitivity analyses are presented. The results show that the prey refuge has a stabilizing effect, that is, the prey refuge is an important factor to maintain the balance between prey and predator population.
期刊介绍：
Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.
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