{"title":"分布时滞反馈Genesio系统的稳定性与Hopf分岔分析","authors":"J. Guan, F. Chen","doi":"10.1109/IWCFTA.2012.19","DOIUrl":null,"url":null,"abstract":"In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical results.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability and Hopf Bifurcation Analysis of Genesio System with Distributed Delays Feedback\",\"authors\":\"J. Guan, F. Chen\",\"doi\":\"10.1109/IWCFTA.2012.19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical results.\",\"PeriodicalId\":354870,\"journal\":{\"name\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 Fifth International Workshop on Chaos-fractals Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2012.19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2012.19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability and Hopf Bifurcation Analysis of Genesio System with Distributed Delays Feedback
In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical results.
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