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Volumn 22, Issue 3, 2000, Pages 249-269

Tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL COMPLEXITY; VIBRATIONS (MECHANICAL);

EID: 0033716338     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008328027179     Document Type: Article
Times cited : (35)

References (20)
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    • H. D. Mittelmann and H. Weber (eds.), Birkhäuser, Basel
    • Langford, W. and Iooss, G., 'Interaction of Hopf and pitchfork bifurcation', in Bifurcation Problems and their Numerical Solution, H. D. Mittelmann and H. Weber (eds.), Birkhäuser, Basel, 1980, pp. 103-134.
    • (1980) Bifurcation Problems and Their Numerical Solution , pp. 103-134
    • Langford, W.1    Iooss, G.2
  • 5
    • 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., 'A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Shil'nikov', Physica D 62, 1993, 230-253.
    • (1993) Physica D , vol.62 , pp. 230-253
    • Freire, E.1    Rodríguez-Luis, A.J.2    Gamero, E.3    Ponce, E.4
  • 7
    • 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., 'Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator', Nonlinear Dynamics 16, 1998, 369-404.
    • (1998) Nonlinear Dynamics , vol.16 , pp. 369-404
    • Algaba, A.1    Freire, E.2    Gamero, E.3    Rodríguez-Luis, A.J.4
  • 9
    • 0009182844 scopus 로고
    • Hopf-zero bifurcation: Normal form calculation and application to an electronic oscillator
    • Barcelona, Spain, August 26-31, C. Perelló et al. (eds.), World Scientific
    • Gamero, E., Freire, E., and Rodríguez-Luis, A. J., 'Hopf-zero bifurcation: Normal form calculation and application to an electronic oscillator', in Proceedings of Equadiff'91, Barcelona, Spain, August 26-31, C. Perelló et al. (eds.), World Scientific, 1991, pp. 517-524.
    • (1991) Proceedings of Equadiff'91 , pp. 517-524
    • Gamero, E.1    Freire, E.2    Rodríguez-Luis, A.J.3
  • 12
    • 0033164120 scopus 로고    scopus 로고
    • A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation
    • Algaba, A., Freire, E., Gamero, E., and Rodríguez-Luis, A. J., 'A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation', Nonlinearity 12, 1999, 1177-1206.
    • (1999) Nonlinearity , vol.12 , pp. 1177-1206
    • Algaba, A.1    Freire, E.2    Gamero, E.3    Rodríguez-Luis, A.J.4
  • 15
    • 84896881561 scopus 로고
    • Local study of planar vector fields: Singularities and their unfolding
    • Structures in Dynamics, H. Broer, F. Dumortier, S. van Strien, and F. Takens (eds.), North-Holland, Amsterdam
    • Dumortier, F., 'Local study of planar vector fields: singularities and their unfolding', in Structures in Dynamics, H. Broer, F. Dumortier, S. van Strien, and F. Takens (eds.), Studies in Mathematical Physics, Vol. 2, North-Holland, Amsterdam, 1991, pp. 161-242.
    • (1991) Studies in Mathematical Physics , vol.2 , pp. 161-242
    • Dumortier, F.1
  • 17
    • 34250127220 scopus 로고
    • T-points: A codimension two heteroclinic bifurcation
    • Glendinning, P. and Sparrow, C., 'T-points: A codimension two heteroclinic bifurcation', Journal of Statistical Physics 43, 1986, 479-488.
    • (1986) Journal of Statistical Physics , vol.43 , pp. 479-488
    • Glendinning, P.1    Sparrow, C.2
  • 18
    • 0000595586 scopus 로고
    • The bifurcations of separatrix contours and chaos
    • Bykov, V., 'The bifurcations of separatrix contours and chaos', Physica D 62, 1993, 290-299.
    • (1993) Physica D , vol.62 , pp. 290-299
    • Bykov, V.1
  • 19
    • 0000036850 scopus 로고
    • Shil'nikov-Hopf bifurcation
    • Hirschberg, P. and Knobloch, E., 'Shil'nikov-Hopf bifurcation', Physica D 62, 1993, 202-216.
    • (1993) Physica D , vol.62 , pp. 202-216
    • Hirschberg, P.1    Knobloch, E.2
  • 20
    • 0347873734 scopus 로고    scopus 로고
    • The non-transverse Shil'nikov-Hopf bifurcation: Uncoupling of homoclinic orbits and homoclinic tangencies
    • Champneys, A. R. and Rodríguez-Luis, A. J., 'The non-transverse Shil'nikov-Hopf bifurcation: Uncoupling of homoclinic orbits and homoclinic tangencies', Physica D 128, 1999, 130-158.
    • (1999) Physica D , vol.128 , pp. 130-158
    • Champneys, A.R.1    Rodríguez-Luis, A.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.