{"title":"m参数化向量场上的Takens-Bogdanov分岔分析","authors":"F. C. Navarro, F. V. Gonzalez, J. Delgado","doi":"10.1142/S0218127410026277","DOIUrl":null,"url":null,"abstract":"Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens–Bogdanov bifurcation.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"29 1","pages":"995-1005"},"PeriodicalIF":0.0000,"publicationDate":"2010-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"Analysis of the Takens-Bogdanov bifurcation on M-Parameterized Vector Fields\",\"authors\":\"F. C. Navarro, F. V. Gonzalez, J. Delgado\",\"doi\":\"10.1142/S0218127410026277\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens–Bogdanov bifurcation.\",\"PeriodicalId\":13688,\"journal\":{\"name\":\"Int. J. Bifurc. Chaos\",\"volume\":\"29 1\",\"pages\":\"995-1005\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Bifurc. Chaos\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S0218127410026277\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0218127410026277","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analysis of the Takens-Bogdanov bifurcation on M-Parameterized Vector Fields
Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens–Bogdanov bifurcation.
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