{"title":"一类新型混沌系统的Hopf分岔","authors":"Kejun Zhuang","doi":"10.5281/ZENODO.1071572","DOIUrl":null,"url":null,"abstract":"In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"1 1","pages":"1094-1097"},"PeriodicalIF":0.0000,"publicationDate":"2010-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Hopf Bifurcation for a New Chaotic System\",\"authors\":\"Kejun Zhuang\",\"doi\":\"10.5281/ZENODO.1071572\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.\",\"PeriodicalId\":23764,\"journal\":{\"name\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"volume\":\"1 1\",\"pages\":\"1094-1097\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5281/ZENODO.1071572\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5281/ZENODO.1071572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
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