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Volumn 202, Issue 1, 2004, Pages 1-31

Hopf-Takens bifurcations and centres

Author keywords

Bautin ideal; Centers; Generic bifurcation diagrams; Hopf singularity; Limit cycles; Lyapunov coefficients; Melnikov functions; Normal forms

Indexed keywords


EID: 3543138370     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.03.018     Document Type: Article
Times cited : (26)

References (11)
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    • Bonin, G.1    Legault, J.2
  • 2
    • 3543088932 scopus 로고    scopus 로고
    • Ordinary Differential Equations with Applications
    • Berlin: Springer
    • Chicone C. Ordinary Differential Equations with Applications in: Texts in Applied Mathematics Vol. 34 1999 Springer Berlin
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    • Chicone, C.1
  • 3
    • 0004005623 scopus 로고
    • Normal Forms and Bifurcation of Planar Vector Fields
    • Cambridge: Cambridge University Press
    • Chow S.N. Li C. Wang D. Normal Forms and Bifurcation of Planar Vector Fields 1994 Cambridge University Press Cambridge
    • (1994)
    • Chow, S.N.1    Li, C.2    Wang, D.3
  • 4
    • 84896881561 scopus 로고
    • Local Study of Planar Vector Fields: Singularities and their Unfoldings
    • H. Broer et al. (Eds.), North-Holland Publishing Co., Amsterdam
    • Dumortier F. Local Study of Planar Vector Fields: Singularities and their Unfoldings, in: H. Broer et al. (Eds.), Structures in Dynamics, 1991, North-Holland Publishing Co., Amsterdam, pp. 161-241
    • (1991) Structures in Dynamics , pp. 161-241
    • Dumortier, F.1
  • 5
    • 0002036676 scopus 로고
    • Generic 3-parameter families of planar vector fields, unfoldings of saddle, focus and elliptic singularities with nilpotent linear parts
    • F. Dumortier, et al(Eds.), Berlin-Heidelberg, New York: Springer
    • Dumortier F. Roussarie R. Sotomayor J. Generic 3-parameter families of planar vector fields, unfoldings of saddle, focus and elliptic singularities with nilpotent linear parts In: Dumortier F. et al.(Eds.) Bifurcations of planar vector fields: Nilpotent singularities and Abelian Integrals Lecture Notes in Mathematics Vol. 1480 1991 1 164 Springer Berlin-Heidelberg, New York
    • (1991) Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals , vol.1480 , pp. 1-164
    • Dumortier, F.1    Roussarie, R.2    Sotomayor, J.3
  • 6
    • 0018530408 scopus 로고
    • Ljapunov Approach to Multiple Hopf Bifurcation
    • Göbber F. Willamowski K.-D. Ljapunov Approach to Multiple Hopf Bifurcation J. Math. Anal. Appl. 71 1979 333-350
    • (1979) J. Math. Anal. Appl. , vol.71 , pp. 333-350
    • Göbber, F.1    Willamowski, K.-D.2
  • 8
    • 0003706484 scopus 로고
    • Applications des varié tés invariantes àla modélisation de l'hétérogénéité en dynamique des populations
    • Thèse, Université de Bourgogne
    • Poggiale J.C. Applications des varié tés invariantes à la modélisation de l'hétérogénéité en dynamique des populations, Thèse, Université de Bourgogne, 1994
    • (1994)
    • Poggiale, J.C.1
  • 10
    • 0001304970 scopus 로고
    • Algebraic and geometric aspects of the theory of polynomial vector fields
    • D. Schlomiuk (Ed.), NATO ASI Series, Mathematical and Physical Sciences Kluwer Academic Publishers, Dordrecht
    • Schlomiuk D. Algebraic and geometric aspects of the theory of polynomial vector fields, in: D. Schlomiuk (Ed.), Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series, Mathematical and Physical Sciences, Vol. 408, 1993, Kluwer Academic Publishers, Dordrecht, pp. 429-463
    • (1993) Bifurcations and Periodic Orbits of Vector Fields , vol.408 , pp. 429-463
    • Schlomiuk, D.1
  • 11
    • 0000857092 scopus 로고
    • Unfoldings of certain singularities of vector fields: Generalised Hopf bifurcations
    • Takens F. Unfoldings of certain singularities of vector fields: generalised Hopf bifurcations J. Differential Equations 14 3 1973 476-493
    • (1973) J. Differential Equations , vol.14 , Issue.3 , pp. 476-493
    • Takens, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.