| COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY |
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| 引用本文： | Bai－sheng Wu (Department of Mathematics,Jilin University,Changchun 130023,China)Tassilo Kupper (Institute of Mathematics,University of Cologne,D-50931 Koln,Germany). COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY[J]. 计算数学(英文版), 1998, 0(5) |
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| 作者姓名： | Bai－sheng Wu (Department of Mathematics Jilin University Changchun 130023 China)Tassilo Kupper (Institute of Mathematics University of Cologne D-50931 Koln Germany) |
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| 作者单位： | Bai－sheng Wu (Department of Mathematics，Jilin University，Changchun 130023，China)Tassilo Kupper (Institute of Mathematics，University of Cologne，D-50931 Koln，Germany) |
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| 摘 要： | 1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss…
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COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY |
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| Abstract: | This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the system.Hence standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.Keyworks: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system |
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| Keywords: | Hopf/pitchfork point Z_2-symmetry Hopf point bifurcation Extended system |
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