{"title":"NEIMARK-SACKER BIFURCATION AND CONTROL OF CHAOTIC BEHAVIOR IN A DISCRETE-TIME PLANT-HERBIVORE SYSTEM","authors":"Ö. Gümüs, A. Selvam, R. Janagaraj","doi":"10.46939/j.sci.arts-22.3-a03","DOIUrl":null,"url":null,"abstract":"In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.","PeriodicalId":54169,"journal":{"name":"Journal of Science and Arts","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Science and Arts","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46939/j.sci.arts-22.3-a03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.
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