{"title":"考虑猎物庇护和捕食者同类相食的Lotka-Volterra捕食-捕食模型的稳定性和有界性分析","authors":"A. Olutimo, O. M. Akinmoladun, Omoko Omoko","doi":"10.47260/jcomod/1212","DOIUrl":null,"url":null,"abstract":"Abstract\n\nIn this paper, a prey-predator system incorporating prey refuge and predator cannibalism is studied. The stability and ultimate boundedness of the analyzed state parameters (y_1,y_2) defining the system are obtained using the Lyapunov’s second or direct method. We construct a suitable complete Lyapunov function for the nonlinear system and demonstrate its efficacy. The method is built upon applying various theoretical Lyapunov functions. By constructing a Lyapunov function which possesses a functional relationship to the the original model system, we give sufficient conditions which ensure the stability and ultimate boundedness of the state parameters describing the nonlinear prey-predator system. We give a numeric example to illustrate the result obtained. \n\nJEL classification numbers: 34C27, 34D23, 34C25.\nKeywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness, Lyapunov’s method.","PeriodicalId":102386,"journal":{"name":"Journal of Computations & Modelling","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Stability and Boundedness Analysis of Lotka-Volterra Prey-Predator Model with Prey Refuge and Predator Cannibalism\",\"authors\":\"A. Olutimo, O. M. Akinmoladun, Omoko Omoko\",\"doi\":\"10.47260/jcomod/1212\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract\\n\\nIn this paper, a prey-predator system incorporating prey refuge and predator cannibalism is studied. The stability and ultimate boundedness of the analyzed state parameters (y_1,y_2) defining the system are obtained using the Lyapunov’s second or direct method. We construct a suitable complete Lyapunov function for the nonlinear system and demonstrate its efficacy. The method is built upon applying various theoretical Lyapunov functions. By constructing a Lyapunov function which possesses a functional relationship to the the original model system, we give sufficient conditions which ensure the stability and ultimate boundedness of the state parameters describing the nonlinear prey-predator system. We give a numeric example to illustrate the result obtained. \\n\\nJEL classification numbers: 34C27, 34D23, 34C25.\\nKeywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness, Lyapunov’s method.\",\"PeriodicalId\":102386,\"journal\":{\"name\":\"Journal of Computations & Modelling\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computations & Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47260/jcomod/1212\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computations & Modelling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47260/jcomod/1212","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability and Boundedness Analysis of Lotka-Volterra Prey-Predator Model with Prey Refuge and Predator Cannibalism
Abstract
In this paper, a prey-predator system incorporating prey refuge and predator cannibalism is studied. The stability and ultimate boundedness of the analyzed state parameters (y_1,y_2) defining the system are obtained using the Lyapunov’s second or direct method. We construct a suitable complete Lyapunov function for the nonlinear system and demonstrate its efficacy. The method is built upon applying various theoretical Lyapunov functions. By constructing a Lyapunov function which possesses a functional relationship to the the original model system, we give sufficient conditions which ensure the stability and ultimate boundedness of the state parameters describing the nonlinear prey-predator system. We give a numeric example to illustrate the result obtained.
JEL classification numbers: 34C27, 34D23, 34C25.
Keywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness, Lyapunov’s method.
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