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Volumn 29, Issue 9, 1999, Pages 49-70

Symbolic software development for computing the normal form of double Hopf bifurcation

Author keywords

1:1 resonance; Non semi simple Hopf bifurcation; Nonlinear transformation; Normal form

Indexed keywords


EID: 0033136097     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00081-3     Document Type: Article
Times cited : (13)

References (16)
  • 5
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    • P. Yu, Computation of normal forms via a perturbation technique, Journal of Sound and Vibration 211, 19-38, (1998).
    • (1998) Journal of Sound and Vibration , vol.211 , pp. 19-38
    • Yu, P.1
  • 6
    • 0032435442 scopus 로고    scopus 로고
    • Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues
    • Q. Bi and P. Yu, Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues, Int. J. Bifurcation and Chaos 8, (1998).
    • (1998) Int. J. Bifurcation and Chaos , vol.8
    • Bi, Q.1    Yu, P.2
  • 8
    • 0000857092 scopus 로고
    • Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcations
    • F. Takens, Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcations, Journal of Differential Equations 14, 476-493, (1973).
    • (1973) Journal of Differential Equations , vol.14 , pp. 476-493
    • Takens, F.1
  • 10
    • 84972948989 scopus 로고
    • Static and dynamic bifurcations associated with a double zero eigenvalues
    • P. Yu and K. Huseyin, Static and dynamic bifurcations associated with a double zero eigenvalues, Dynamics and Stability of Systems 1, 73-86, (1986).
    • (1986) Dynamics and Stability of Systems , vol.1 , pp. 73-86
    • Yu, P.1    Huseyin, K.2
  • 11
    • 51649178043 scopus 로고
    • Singularities of vector fields
    • F. Takens, Singularities of vector fields, Publ. Math. IHES 43, 47-100, (1974).
    • (1974) Publ. Math. IHES , vol.43 , pp. 47-100
    • Takens, F.1
  • 12
    • 0023995274 scopus 로고
    • On bifurcations into non-resonant quasi-periodic motions
    • K. Huseyin and P. Yu, On bifurcations into non-resonant quasi-periodic motions, Applied Mathematical Modelling 12, 189-201, (1988).
    • (1988) Applied Mathematical Modelling , vol.12 , pp. 189-201
    • Huseyin, K.1    Yu, P.2
  • 13
    • 0025442956 scopus 로고
    • Dynamic behavior of an autonomous system with three pairs of pure imaginary eigenvalues
    • P. Yu and K. Huseyin, Dynamic behavior of an autonomous system with three pairs of pure imaginary eigenvalues, International Journal of Systems and Science 21, 993-1024, (1990).
    • (1990) International Journal of Systems and Science , vol.21 , pp. 993-1024
    • Yu, P.1    Huseyin, K.2
  • 14
    • 0003160780 scopus 로고
    • On phase-locked motions associated with strong resonance
    • P. Yu and K. Huseyin, On phase-locked motions associated with strong resonance, Quarterly of Applied Mathematics 51, 91-100, (1993).
    • (1993) Quarterly of Applied Mathematics , vol.51 , pp. 91-100
    • Yu, P.1    Huseyin, K.2
  • 15
    • 0002232810 scopus 로고
    • A simple global characterization for normal forms of singular vector fields
    • C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet and G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica D 29, 95-127, (1987).
    • (1987) Physica D , vol.29 , pp. 95-127
    • Elphick, C.1    Tirapegui, E.2    Brachet, M.E.3    Coullet, P.4    Iooss, G.5
  • 16
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    • Strongly resonant Hopf bifurcation and vortex induced vibrations
    • John Wiley and Sons, New York
    • W.F. Langford and K. Zhan, Strongly resonant Hopf bifurcation and vortex induced vibrations, In Nonlinearity and Chaos in Engineering Dynamics, John Wiley and Sons, New York, (1994).
    • (1994) Nonlinearity and Chaos in Engineering Dynamics
    • Langford, W.F.1    Zhan, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.