Hypernormal form for the hopf-zero bifurcation

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 10, 1998, Pages 1857-1887

  Algaba, A ^a   Freire, E ^b   Gamero, E ^b  

^a UNIVERSITY OF HUELVA   (Spain)

^b UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040633552     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001583     Document Type: Article

References (14)

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2. Algaba, A., Freire, E., Gamero, E. & Rodríguez-Luis, A. J. [1998b] "On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations," preprint.
3. Algaba, A., Freire, E., Gamero, E. & Rodríguez-Luis, A. J. [1998c] "A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation," preprint.
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10. Langford, W. F. & Iooss, G. [1980] "Interaction of Hopf and pitchfork bifurcation," in Bifurcation Problems and their Numerical Solution, eds. Mittelmann, H. D. & Weber, H. (Birkhäuser, Basel), pp. 103-134.
11. Nayfeh, A. H. [1993] Method of Normal Forms (John Wiley, NY).
12. Peckham, B. B., Frouzakis, C. E. & Kevrekidis, I. G. [1995] "Bananas and banana splits: A parametric degeneracy in the Hopf bifurcation for maps," SIAM J. Math. Anal. 26(1), 190-217.
13. Pivka, L., Wu, C. W. & Huang, A. [1996] "Lorenz equation and Chua's equation," Int. J. Bifurcation and Chaos 6(12B), 2443-2489.
14. Ushiki, S. [1984] "Normal forms for singularities of vector fields," Jpn. J. Appl. Math. 1, 1-37.