{"title":"Neimark-Sacker Bifurcation of a Third Order Difference Equation","authors":"M. Aloqeili, A. Shareef","doi":"10.33401/FUJMA.527572","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Journal of Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33401/FUJMA.527572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.
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