{"title":"改进Leslie-Gower捕食-捕食模型的Hopf分岔和图灵不稳定性","authors":"Yan Meng, Guangwu Wen, L. Min","doi":"10.1109/ISB.2013.6623798","DOIUrl":null,"url":null,"abstract":"In this paper, we study a modified Leslie-Gower prey-predator model in the presence of nonlinear harvesting in prey subject to the Neumann boundary condition. Our results reveal the conditions on the parameters so that the periodic solution exist surrounding the interior equilibrium. Furthermore, the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. For the model with the Neumann boundary condition, Turing instability of the interior equilibrium solution is studied. In particular, Turing instability region regarding the parameters is established. Numerical simulations are carried out to demonstrate the results obtained.","PeriodicalId":151775,"journal":{"name":"2013 7th International Conference on Systems Biology (ISB)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hopf bifurcation and Turing instability in a modified Leslie-Gower prey-predator model\",\"authors\":\"Yan Meng, Guangwu Wen, L. Min\",\"doi\":\"10.1109/ISB.2013.6623798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study a modified Leslie-Gower prey-predator model in the presence of nonlinear harvesting in prey subject to the Neumann boundary condition. Our results reveal the conditions on the parameters so that the periodic solution exist surrounding the interior equilibrium. Furthermore, the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. For the model with the Neumann boundary condition, Turing instability of the interior equilibrium solution is studied. In particular, Turing instability region regarding the parameters is established. Numerical simulations are carried out to demonstrate the results obtained.\",\"PeriodicalId\":151775,\"journal\":{\"name\":\"2013 7th International Conference on Systems Biology (ISB)\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 7th International Conference on Systems Biology (ISB)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISB.2013.6623798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 7th International Conference on Systems Biology (ISB)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISB.2013.6623798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hopf bifurcation and Turing instability in a modified Leslie-Gower prey-predator model
In this paper, we study a modified Leslie-Gower prey-predator model in the presence of nonlinear harvesting in prey subject to the Neumann boundary condition. Our results reveal the conditions on the parameters so that the periodic solution exist surrounding the interior equilibrium. Furthermore, the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. For the model with the Neumann boundary condition, Turing instability of the interior equilibrium solution is studied. In particular, Turing instability region regarding the parameters is established. Numerical simulations are carried out to demonstrate the results obtained.
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