{"title":"一类具有猎物庇护和扩散的捕食-食饵系统的分岔分析","authors":"Chaoming Huang, Yiping Lin","doi":"10.1109/IWCFTA.2012.40","DOIUrl":null,"url":null,"abstract":"In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. Hopf bifurcation is occurred. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bifurcation Analysis for a Predator-Prey System with Prey Refuge and Diffusion\",\"authors\":\"Chaoming Huang, Yiping Lin\",\"doi\":\"10.1109/IWCFTA.2012.40\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. Hopf bifurcation is occurred. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed.\",\"PeriodicalId\":354870,\"journal\":{\"name\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2012.40\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2012.40","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bifurcation Analysis for a Predator-Prey System with Prey Refuge and Diffusion
In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. Hopf bifurcation is occurred. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed.