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Volumn 18, Issue 2, 1999, Pages 129-158

Detection of bifurcation structures by higher-order averaging for Duffing's equation

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTER AIDED SOFTWARE ENGINEERING; COMPUTER SIMULATION; OSCILLATORS (ELECTRONIC); RESONANCE;

EID: 0032649107     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008371723533     Document Type: Article
Times cited : (19)

References (27)
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    • (1985) Physics Letters A , vol.107 , pp. 351-355
    • Parlitz, U.1    Lauterborn, W.2
  • 4
    • 19044385619 scopus 로고
    • Resonances and torsion numbers of driven dissipative nonlinear oscillators
    • Parlitz, U. and Lauterborn, W., 'Resonances and torsion numbers of driven dissipative nonlinear oscillators', Zeitschrift für Naturforschung A 41, 1986, 605-614.
    • (1986) Zeitschrift für Naturforschung A , vol.41 , pp. 605-614
    • Parlitz, U.1    Lauterborn, W.2
  • 7
    • 0004149831 scopus 로고
    • Addison-Wesley, Redwood City, 3rd edn., Wolfram Media/Cambridge University Press, Champaign/Cambridge
    • Wolfram, S., The Mathematica Book, 2nd edn, Addison-Wesley, Redwood City, 1991; 3rd edn., Wolfram Media/Cambridge University Press, Champaign/Cambridge, 1996.
    • (1991) The Mathematica Book, 2nd Edn
    • Wolfram, S.1
  • 13
    • 0009287703 scopus 로고
    • Qualitative theory of nonlinear resonance by averaging and dynamical systems methods
    • U. Kirchgraber, and H. O. Walther (eds.), Wiley, New York
    • Murdock, J., 'Qualitative theory of nonlinear resonance by averaging and dynamical systems methods', in Dynamics Reported, Vol. 1, U. Kirchgraber, and H. O. Walther (eds.), Wiley, New York, 1988, pp. 91-172.
    • (1988) Dynamics Reported , vol.1 , pp. 91-172
    • Murdock, J.1
  • 15
    • 0006905161 scopus 로고    scopus 로고
    • Higher-order averaging and ultra-subharmonics in forced oscillators
    • Yagasaki, K., 'Higher-order averaging and ultra-subharmonics in forced oscillators', Journal of Sound and Vibration 210, 1998, 529-553.
    • (1998) Journal of Sound and Vibration , vol.210 , pp. 529-553
    • Yagasaki, K.1
  • 19
    • 0016892501 scopus 로고
    • The bifurcations of Duffing's equation: An application of catastrophe theory
    • Holmes, P. J. and Rand, D. A., 'The bifurcations of Duffing's equation: An application of catastrophe theory', Journal of Sound and Vibration 44, 1976, 237-253.
    • (1976) Journal of Sound and Vibration , vol.44 , pp. 237-253
    • Holmes, P.J.1    Rand, D.A.2
  • 20
    • 0030573385 scopus 로고    scopus 로고
    • Second-order averaging and Melnikov analyses for forced non-linear oscillators
    • Yagasaki, K., 'Second-order averaging and Melnikov analyses for forced non-linear oscillators', Journal of Sound and Vibration 190, 1996, 587-609.
    • (1996) Journal of Sound and Vibration , vol.190 , pp. 587-609
    • Yagasaki, K.1
  • 21
    • 0002747396 scopus 로고
    • AUTO: Software for continuation and bifurcation problems in ordinary differential equations
    • California Institute of Technology
    • Doedel, E. and Kernévez, J., 'AUTO: Software for continuation and bifurcation problems in ordinary differential equations', Applied Mathematics Reports, California Institute of Technology, 1986.
    • (1986) Applied Mathematics Reports
    • Doedel, E.1    Kernévez, J.2
  • 23
    • 0030416838 scopus 로고    scopus 로고
    • The Melnikov theory for subharmonics and their bifurcations in forced oscillations
    • Yagasaki, K., 'The Melnikov theory for subharmonics and their bifurcations in forced oscillations', SIAM Journal on Applied Mathematics 56, 1996, 1720-1765.
    • (1996) SIAM Journal on Applied Mathematics , vol.56 , pp. 1720-1765
    • Yagasaki, K.1
  • 24
    • 0025206791 scopus 로고
    • Averaging using elliptic functions: Approximation of limit cycles
    • Coppola, V. T. and Rand, R. H., 'Averaging using elliptic functions: Approximation of limit cycles', Acta Mechanica 81, 1990, 125-142.
    • (1990) Acta Mechanica , vol.81 , pp. 125-142
    • Coppola, V.T.1    Rand, R.H.2
  • 25
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    • MACSYMA program to implement averaging using elliptic functions
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    • Coppola, V. T. and Rand, R. H., 'MACSYMA program to implement averaging using elliptic functions', in Computer Aided Proofs in Analysis, K. R. Meyer and D. S. Schmidt (eds.), Springer-Verlag, New York, 1991. pp. 71-89.
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    • Coppola, V.T.1    Rand, R.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.