{"title":"Dynamical behaviours of Bazykin-Berezovskaya model with fractional-order and its discretization","authors":"M. H. Akrami","doi":"10.22034/CMDE.2020.30802.1460","DOIUrl":null,"url":null,"abstract":"This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviours than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulation verify the analytical results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2020.30802.1460","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviours than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulation verify the analytical results.
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