{"title":"Dynamical Analysis of a Predator–Prey Model with Additive Allee Effect and Migration","authors":"Xinhao Huang, Lijuan Chen, Yue Xia, Fengde Chen","doi":"10.1142/s0218127423501791","DOIUrl":null,"url":null,"abstract":"In this paper, a predator–prey model in which the prey has the additive Allee effect and the predator has artificially controlled migration is proposed. When the system introduces additive Allee effect and artificially controlled migration, more complicated dynamical behavior is obtained. The system can undergo saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Two limit cycles are found and discussed. The influence of the additive Allee effect and artificially controlled migration on the dynamics of the system is also presented. In detail, when the Allee effect is large, the prey will become extinct. When the artificially controlled migration rate is larger, the intensity of the prey (pest) will be smaller and the intensity of the predator will be larger. This indicates that artificially controlled migration can be effectively used to control the pest.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"68 6","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Bifurcation and Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218127423501791","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a predator–prey model in which the prey has the additive Allee effect and the predator has artificially controlled migration is proposed. When the system introduces additive Allee effect and artificially controlled migration, more complicated dynamical behavior is obtained. The system can undergo saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Two limit cycles are found and discussed. The influence of the additive Allee effect and artificially controlled migration on the dynamics of the system is also presented. In detail, when the Allee effect is large, the prey will become extinct. When the artificially controlled migration rate is larger, the intensity of the prey (pest) will be smaller and the intensity of the predator will be larger. This indicates that artificially controlled migration can be effectively used to control the pest.
期刊介绍：
The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering.
The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.
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