{"title":"Hopf Bifurcation of Three-Dimensional Quadratic Jerk System","authors":"Tahsin I. Rasul, Rizgar H. Salih","doi":"10.21123/bsj.2023.8945","DOIUrl":null,"url":null,"abstract":"This paper is devoted to investigating the Hopf bifurcation of a three-dimensional quadratic jerk system. The stability of the singular points, the appearance of the Hopf bifurcation and the limit cycles of the system are studied. Additionally, the Liapunov quantities technique is used to study the cyclicity of the system and find how many limit cycles can be bifurcated from the Hopf points. Due to the computational load required for computing Liapunov quantities, some parameters are fixed. Currently, the analysis shows that three limit cycles can be bifurcated from the Hopf points. The results presented in this study are verified using MAPLE program.","PeriodicalId":8687,"journal":{"name":"Baghdad Science Journal","volume":"2019 37","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Baghdad Science Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21123/bsj.2023.8945","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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Abstract
This paper is devoted to investigating the Hopf bifurcation of a three-dimensional quadratic jerk system. The stability of the singular points, the appearance of the Hopf bifurcation and the limit cycles of the system are studied. Additionally, the Liapunov quantities technique is used to study the cyclicity of the system and find how many limit cycles can be bifurcated from the Hopf points. Due to the computational load required for computing Liapunov quantities, some parameters are fixed. Currently, the analysis shows that three limit cycles can be bifurcated from the Hopf points. The results presented in this study are verified using MAPLE program.
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