메뉴 건너뛰기




Volumn 12, Issue 4, 1999, Pages 1177-1206

A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033164120     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/4/324     Document Type: Article
Times cited : (34)

References (22)
  • 2
    • 0032136401 scopus 로고    scopus 로고
    • Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator
    • Algaba A, Freire E, Gamero E and Rodríguez-Luis A J 1998 Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator Nonlinear Dynam. 16 369-404
    • (1998) Nonlinear Dynam. , vol.16 , pp. 369-404
    • Algaba, A.1    Freire, E.2    Gamero, E.3    Rodríguez-Luis, A.J.4
  • 7
    • 0001231858 scopus 로고
    • Subordinate Shil'nikov bifurcations near some singularities of vector fields having low codimension
    • Broer H and Vegter G 1984 Subordinate Shil'nikov bifurcations near some singularities of vector fields having low codimension Ergod. Theor. Dynam. Syst. 4 509-25
    • (1984) Ergod. Theor. Dynam. Syst. , vol.4 , pp. 509-525
    • Broer, H.1    Vegter, G.2
  • 8
    • 0009205863 scopus 로고
    • On the Bogdanov-Takens bifurcation for planar diffeomorphisms
    • Singapore: World Scientific
    • Broer H W, Roussarie R and Simó C 1993 On the Bogdanov-Takens bifurcation for planar diffeomorphisms Proc. Equadiff'91 (Singapore: World Scientific) pp 81-92
    • (1993) Proc. Equadiff'91 , pp. 81-92
    • Broer, H.W.1    Roussarie, R.2    Simó, C.3
  • 9
    • 0003303854 scopus 로고
    • Auto94: Software for continuation and bifurcation problems in ODE
    • California Institute of Technology
    • Doedel E, Wang X and Fairgrieve T 1995 Auto94: Software for continuation and bifurcation problems in ODE Applied Mathematics Report (User's Manual) (California Institute of Technology)
    • (1995) Applied Mathematics Report (User's Manual)
    • Doedel, E.1    Wang, X.2    Fairgrieve, T.3
  • 10
    • 84896881561 scopus 로고
    • Local study of planar vector fields: Singularities and their unfolding
    • ed H W Broer et al Amsterdam: North Holland
    • Dumortier F 1991 Local study of planar vector fields: singularities and their unfolding Structures in Dynamics, Studies in Maths and Physics vol 2 ed H W Broer et al pp 161-242 (Amsterdam: North Holland)
    • (1991) Structures in Dynamics, Studies in Maths and Physics , vol.2 , pp. 161-242
    • Dumortier, F.1
  • 11
    • 2742611797 scopus 로고
    • A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Shil'nikov
    • Freire E, Rodríguez-Luis A J, Gamero E and Ponce E 1993 A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Shil'nikov. Physica D 62 230-53
    • (1993) Physica D , vol.62 , pp. 230-253
    • Freire, E.1    Rodríguez-Luis, A.J.2    Gamero, E.3    Ponce, E.4
  • 13
    • 0002895479 scopus 로고
    • Local birth of homoclinic chaos
    • Gaspard P 1993 Local birth of homoclinic chaos. Physica D 62 94-122
    • (1993) Physica D , vol.62 , pp. 94-122
    • Gaspard, P.1
  • 15
    • 0000036850 scopus 로고
    • Shil'nikov-Hopf bifurcation
    • Hirschberg P and Knobloch E 1993 Shil'nikov-Hopf bifurcation Physica D 62 202-16
    • (1993) Physica D , vol.62 , pp. 202-216
    • Hirschberg, P.1    Knobloch, E.2
  • 16
    • 0000868937 scopus 로고    scopus 로고
    • Codimension-three unfoldings of reflectionally symmetric planar vector fields
    • Krauskopf B and Rousseau C 1997 Codimension-three unfoldings of reflectionally symmetric planar vector fields Nonlinearity 10 1115-50
    • (1997) Nonlinearity , vol.10 , pp. 1115-1150
    • Krauskopf, B.1    Rousseau, C.2
  • 18
    • 21844490940 scopus 로고
    • Bananas and banana splits: A parametric degeneracy in the Hopf bifurcation for maps
    • Peckham B B, Frouzakis C E and Kevrekidis I G 1995 Bananas and banana splits: a parametric degeneracy in the Hopf bifurcation for maps. SIAM J. Math. Anal. 26 190-217
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 190-217
    • Peckham, B.B.1    Frouzakis, C.E.2    Kevrekidis, I.G.3
  • 19
    • 0002734682 scopus 로고
    • Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral
    • Schecter S 1990 Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral Nonlinearity 3 79-99
    • (1990) Nonlinearity , vol.3 , pp. 79-99
    • Schecter, S.1
  • 20
    • 38248998562 scopus 로고
    • Pitchfork bifurcation with a heteroclinic orbit: Normal form, recognition criteria and universal unfolding
    • Schecter S 1993 Pitchfork bifurcation with a heteroclinic orbit: normal form, recognition criteria and universal unfolding J. Diff. Eqns 105 63-99
    • (1993) J. Diff. Eqns , vol.105 , pp. 63-99
    • Schecter, S.1
  • 21
    • 51649178043 scopus 로고
    • Singularities of vector fields
    • Takens F 1974 Singularities of vector fields Publ. Math. IHES 43 47-58
    • (1974) Publ. Math. IHES , vol.43 , pp. 47-58
    • Takens, F.1
  • 22
    • 84971708912 scopus 로고
    • Uniqueness of limit cycles in polynomial systems with algebraic invariants
    • Zegeling A and Kooij R E 1994 Uniqueness of limit cycles in polynomial systems with algebraic invariants Bull. Aus. Math. Soc. 49 7-20
    • (1994) Bull. Aus. Math. Soc. , vol.49 , pp. 7-20
    • Zegeling, A.1    Kooij, R.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.