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Volumn 27, Issue 3, 2006, Pages 647-665

On period doubling bifurcations of cycles and the harmonic balance method

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; COMPUTER SOFTWARE; FREQUENCY MULTIPLYING CIRCUITS; GRAPH THEORY; HARMONIC ANALYSIS; MATRIX ALGEBRA; PARAMETER ESTIMATION;

EID: 23144432847     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.04.061     Document Type: Article
Times cited : (36)

References (29)
  • 1
    • 84971124048 scopus 로고
    • Harmonic balance and the Hopf bifurcation theorem
    • D.J. Allwright Harmonic balance and the Hopf bifurcation theorem Math Proc Cambridge Philos Soc 82 1977 453 467
    • (1977) Math Proc Cambridge Philos Soc , vol.82 , pp. 453-467
    • Allwright, D.J.1
  • 2
    • 0000730838 scopus 로고
    • Symmetry-breaking and first period-doubling following a Hopf bifurcation in a three dimensional system
    • M. Belhaq, and M. Houssni Symmetry-breaking and first period-doubling following a Hopf bifurcation in a three dimensional system Mech Res Commun 22 3 1995 221 231
    • (1995) Mech Res Commun , vol.22 , Issue.3 , pp. 221-231
    • Belhaq, M.1    Houssni, M.2
  • 5
    • 0035501825 scopus 로고    scopus 로고
    • Detecting period-doubling bifurcation: An approximate monodromy matrix approach
    • D.W. Berns, J.L. Moiola, and G. Chen Detecting period-doubling bifurcation: an approximate monodromy matrix approach Automatica 37 2001 1787 1795
    • (2001) Automatica , vol.37 , pp. 1787-1795
    • Berns, D.W.1    Moiola, J.L.2    Chen, G.3
  • 6
    • 0032633388 scopus 로고    scopus 로고
    • Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach
    • F. Bonani, and M. Gilli Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach IEEE Trans Circ Syst I: Fundam Theory Appl 46 8 1999 881 890
    • (1999) IEEE Trans Circ Syst I: Fundam Theory Appl , vol.46 , Issue.8 , pp. 881-890
    • Bonani, F.1    Gilli, M.2
  • 7
    • 0036493990 scopus 로고    scopus 로고
    • Subharmonics and chaos in switched reluctance motor drives
    • J.H. Chen, K.T. Chau, C.C. Chan, and Q. Jiang Subharmonics and chaos in switched reluctance motor drives IEEE Trans Energy Convers 17 l 2002 73 78
    • (2002) IEEE Trans Energy Convers , vol.17 , Issue.50 , pp. 73-78
    • Chen, J.H.1    Chau, K.T.2    Chan, C.C.3    Jiang, Q.4
  • 8
    • 0142153915 scopus 로고    scopus 로고
    • An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom
    • K.W. Chung, C.L. Chan, and J. Xu An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom J Sound Vib 267 2003 787 808
    • (2003) J Sound Vib , vol.267 , pp. 787-808
    • Chung, K.W.1    Chan, C.L.2    Xu, J.3
  • 10
    • 17044412917 scopus 로고    scopus 로고
    • Double Hopf bifurcation analysis using frequency domain methods
    • G.R. Itovich, and J.L. Moiola Double Hopf bifurcation analysis using frequency domain methods Nonlinear Dynam 39 2005 235 258
    • (2005) Nonlinear Dynam , vol.39 , pp. 235-258
    • Itovich, G.R.1    Moiola, J.L.2
  • 12
    • 4544313738 scopus 로고
    • Continuation techniques and interactive software for bifurcation analysis of ODE's and iterated maps
    • A.I. Khibnik, Y.A. Kuznetsov, V.V. Levitin, and E.V. Nikolaev Continuation techniques and interactive software for bifurcation analysis of ODE's and iterated maps Physica D 62 1993 360 371
    • (1993) Physica D , vol.62 , pp. 360-371
    • Khibnik, A.I.1    Kuznetsov, Y.A.2    Levitin, V.V.3    Nikolaev, E.V.4
  • 14
    • 0017450097 scopus 로고
    • The generalized Nyquist stability criterion and multivariable root loci
    • A.G. MacFarlane, and I. Postlethwaite The generalized Nyquist stability criterion and multivariable root loci Int J Control 25 1977 81 127
    • (1977) Int J Control , vol.25 , pp. 81-127
    • MacFarlane, A.G.1    Postlethwaite, I.2
  • 17
    • 0018452921 scopus 로고
    • The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
    • A.I. Mees, and L. Chua The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems IEEE Trans Circ Syst 6 4 1979 235 254
    • (1979) IEEE Trans Circ Syst , vol.6 , Issue.4 , pp. 235-254
    • Mees, A.I.1    Chua, L.2
  • 20
    • 0242579395 scopus 로고    scopus 로고
    • Dynamical regimes underlying epileptiform events: Role of instabilities and bifurcation in brain activity
    • J. Perez Velázquez, M. Cortez, O. Carter Snead III, and R. Wennberg Dynamical regimes underlying epileptiform events: role of instabilities and bifurcation in brain activity Physica D 16 2003 205 220
    • (2003) Physica D , vol.16 , pp. 205-220
    • Velázquez, J.P.1    Cortez, M.2    Snead III, O.C.3    Wennberg, R.4
  • 21
    • 38249021737 scopus 로고
    • Analytical approximation for period-doubling following a Hopf bifurcation
    • R.H. Rand Analytical approximation for period-doubling following a Hopf bifurcation Mech Res Commun 16 2 1989 117 123
    • (1989) Mech Res Commun , vol.16 , Issue.2 , pp. 117-123
    • Rand, R.H.1
  • 22
    • 10444269384 scopus 로고    scopus 로고
    • Detection of limit cycle bifurcations using harmonic balance methods
    • F.I. Robbio, D.M. Alonso, and J.L. Moiola Detection of limit cycle bifurcations using harmonic balance methods Int J Bifurcat Chaos 14 10 2004 3647 3654
    • (2004) Int J Bifurcat Chaos , vol.14 , Issue.10 , pp. 3647-3654
    • Robbio, F.I.1    Alonso, D.M.2    Moiola, J.L.3
  • 23
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O. Rössler An equation for continuous chaos Phys Lett A 57 5 1976 397 398
    • (1976) Phys Lett A , vol.57 , Issue.5 , pp. 397-398
    • Rössler, O.1
  • 25
    • 0036210376 scopus 로고    scopus 로고
    • Poincaré mapping for detecting abnormal dynamics of cardiac repolarization
    • P. Strumillo, and J. Ruta Poincaré mapping for detecting abnormal dynamics of cardiac repolarization IEEE Eng Med Bio Mag 21 1 2002 62 65
    • (2002) IEEE Eng Med Bio Mag , vol.21 , Issue.1 , pp. 62-65
    • Strumillo, P.1    Ruta, J.2
  • 26
    • 0029406015 scopus 로고
    • Bifurcation, chaos and voltage collapse in power systems
    • C. Tan, M. Varghese, P. Varaiya, and F. Wu Bifurcation, chaos and voltage collapse in power systems Proc IEEE 83 11 1995 1484 1496
    • (1995) Proc IEEE , vol.83 , Issue.11 , pp. 1484-1496
    • Tan, C.1    Varghese, M.2    Varaiya, P.3    Wu, F.4
  • 27
    • 0030235714 scopus 로고    scopus 로고
    • Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
    • A. Tesi, E.H. Abed, R. Genesio, and H.O. Wang Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics Automatica 2 1996 1255 1271
    • (1996) Automatica , vol.2 , pp. 1255-1271
    • Tesi, A.1    Abed, E.H.2    Genesio, R.3    Wang, H.O.4
  • 29
    • 0031678169 scopus 로고    scopus 로고
    • On the computation of characteristic multipliers for predicting limit cycle bifurcations
    • G. Torrini, R. Genesio, and A. Tesi On the computation of characteristic multipliers for predicting limit cycle bifurcations Chaos, Solitons & Fractals 9 l/2 1998 121 133
    • (1998) Chaos, Solitons & Fractals , vol.9 , Issue.502 , pp. 121-133
    • Torrini, G.1    Genesio, R.2    Tesi, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.