{"title":"Joint Impact of Maturation Delay and Fear Effect on the Population Dynamics of a Predator-Prey System","authors":"Xiaoke Ma, Ying Su, Xingfu Zou","doi":"10.1137/23m1596569","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. <br/> Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1596569","RegionNum":4,"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
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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