{"title":"二维离散猎物-捕食者模型的定性行为","authors":"Messaoud Berkal, Juan F. Navarro","doi":"10.1002/cmm4.1193","DOIUrl":null,"url":null,"abstract":"<p>In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1193","citationCount":"7","resultStr":"{\"title\":\"Qualitative behavior of a two-dimensional discrete-time prey–predator model\",\"authors\":\"Messaoud Berkal, Juan F. Navarro\",\"doi\":\"10.1002/cmm4.1193\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.</p>\",\"PeriodicalId\":100308,\"journal\":{\"name\":\"Computational and Mathematical Methods\",\"volume\":\"3 6\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1193\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational and Mathematical Methods\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/cmm4.1193\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cmm4.1193","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Qualitative behavior of a two-dimensional discrete-time prey–predator model
In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.
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