메뉴 건너뛰기




Volumn 14, Issue 3, 2004, Pages 951-970

On semi-analytical procedure for detecting limit cycle bifurcations

Author keywords

Harmonic balance; Hopf bifurcation; Limit cycles; Monodromy matrix; Period doubling

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK; FREQUENCY DOMAIN ANALYSIS; HARMONIC ANALYSIS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; THEOREM PROVING;

EID: 3142667702     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404009703     Document Type: Article
Times cited : (5)

References (24)
  • 1
    • 0000730838 scopus 로고
    • Symmetry-breaking and first period-doubling following a Hopf bifurcation in a three-dimensional system
    • Belhaq, M. & Houssni, M. [1995] "Symmetry-breaking and first period-doubling following a Hopf bifurcation in a three-dimensional system," Mech. Res. Commun. 22, 221-231.
    • (1995) Mech. Res. Commun. , vol.22 , pp. 221-231
    • Belhaq, M.1    Houssni, M.2
  • 2
    • 0040187670 scopus 로고    scopus 로고
    • Analytical prediction of the two first period-doublings in a three-dimensional system
    • Belhaq, M., Houssni, M., Freire, E. & Rodríguez-Luis, A. J. [2000] "Analytical prediction of the two first period-doublings in a three-dimensional system," Int. J. Bifurcation and Chaos 10, 1497-1508.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 1497-1508
    • Belhaq, M.1    Houssni, M.2    Freire, E.3    Rodríguez-Luis, A.J.4
  • 3
    • 0035501825 scopus 로고    scopus 로고
    • Detecting period-doubling bifurcation: An approximate monodromy matrix approach
    • Berns, D. W., Moiola, J. L. & Chen, G. [2001] "Detecting period-doubling bifurcation: an approximate monodromy matrix approach," Automatica 37, 1787-1795.
    • (2001) Automatica , vol.37 , pp. 1787-1795
    • Berns, D.W.1    Moiola, J.L.2    Chen, G.3
  • 4
    • 0032633388 scopus 로고    scopus 로고
    • Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach
    • Bonani, F. & Gilli, M. [1999] "Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach," IEEE Trans. Circuits Sysi.-I 46, 881-890.
    • (1999) IEEE Trans. Circuits Sysi.-I , vol.46 , pp. 881-890
    • Bonani, F.1    Gilli, M.2
  • 5
    • 0030380912 scopus 로고    scopus 로고
    • Asymptotic formulas in nearly sinusoidal nonlinear oscillators
    • Buonomo, A. & Di Bello, C. [1996] "Asymptotic formulas in nearly sinusoidal nonlinear oscillators," IEEE Trans. Circuits Syst.-I 43, 953-963.
    • (1996) IEEE Trans. Circuits Syst.-I , vol.43 , pp. 953-963
    • Buonomo, A.1    Di Bello, C.2
  • 6
    • 0032157864 scopus 로고    scopus 로고
    • Symbolic computation of local stability and bifurcation surfaces for nonlinear time-periodic systems
    • Butcher, E. A. & Sinha, S. C. [1998] "Symbolic computation of local stability and bifurcation surfaces for nonlinear time-periodic systems," Nonlin. Dyn. 17, 1-21.
    • (1998) Nonlin. Dyn. , vol.17 , pp. 1-21
    • Butcher, E.A.1    Sinha, S.C.2
  • 7
    • 0034238522 scopus 로고    scopus 로고
    • Bifurcation analysis of Chen's equation
    • Chen, G. & Ueta, T. [2000] "Bifurcation analysis of Chen's equation," Int. J. Bifurcation and Chaos 10, 1917-1931.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 1917-1931
    • Chen, G.1    Ueta, T.2
  • 9
    • 0004537888 scopus 로고    scopus 로고
    • University of Pittsburg, Pittsburg, USA
    • Ermentrout, B. [2001] "XPPAUT5.0 - the differential equation tool" (available via HTTP at: www.math.pitt.edu/~bard/xpp/xpp.html), University of Pittsburg, Pittsburg, USA.
    • (2001) XPPAUT5.0 - The Differential Equation Tool
    • Ermentrout, B.1
  • 10
    • 0034967327 scopus 로고    scopus 로고
    • Computing periodic orbits and their bifurcations with automatic differentiation
    • Guckenheimer, J. & Meloon, B. [2000] "Computing periodic orbits and their bifurcations with automatic differentiation," SIAM J. Sci. Comput. 22, 951-985.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 951-985
    • Guckenheimer, J.1    Meloon, B.2
  • 11
    • 4544313738 scopus 로고
    • Continuation techniques and interactive software for bifurcation analysis of ODE's and iterated maps
    • Khibnik, A. I., Kuznetsov, Yu. A., Levitin, V. V. & Nikolaev, E. V. [1993] "Continuation techniques and interactive software for bifurcation analysis of ODE's and iterated maps," Physica D62, 360-371.
    • (1993) Physica , vol.D62 , pp. 360-371
    • Khibnik, A.I.1    Kuznetsov, Yu.A.2    Levitin, V.V.3    Nikolaev, E.V.4
  • 12
    • 0018452921 scopus 로고
    • The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
    • Mees, A. I. & Chua, L. O. [1979] "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst. CAS-28, 235-254.
    • (1979) IEEE Trans. Circuits Syst. , vol.CAS-28 , pp. 235-254
    • Mees, A.I.1    Chua, L.O.2
  • 15
    • 0034238507 scopus 로고    scopus 로고
    • Bifurcation dynamics of three-dimensional systems
    • Phillipson, P. E. & Schuster, P. [2000] "Bifurcation dynamics of three-dimensional systems," Int. J. Bifurcation and Chaos 10, 1787-1804.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 1787-1804
    • Phillipson, P.E.1    Schuster, P.2
  • 16
    • 38249021737 scopus 로고
    • Analytical approximation for period-doubling following a Hopf bifurcation
    • Rand, R. H. [1989] "Analytical approximation for period-doubling following a Hopf bifurcation," Mech. Res. Commun. 16, 117-123.
    • (1989) Mech. Res. Commun. , vol.16 , pp. 117-123
    • Rand, R.H.1
  • 18
    • 0031237138 scopus 로고    scopus 로고
    • Symbolic computation of fundamental solution matrices for linear time-periodic dynamical systems
    • Sinha, S. C. &: Butcher, E. A. [1997] "Symbolic computation of fundamental solution matrices for linear time-periodic dynamical systems," J. Sound Vibr. 206, 61-85.
    • (1997) J. Sound Vibr. , vol.206 , pp. 61-85
    • Sinha, S.C.1    Butcher, E.A.2
  • 19
    • 33751555569 scopus 로고
    • Some simple chaotic flows
    • Sprott, J. C. [1994] "Some simple chaotic flows," Phys. Rev. E50, 647-650.
    • (1994) Phys. Rev. , vol.E50 , pp. 647-650
    • Sprott, J.C.1
  • 20
    • 0030235714 scopus 로고    scopus 로고
    • Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
    • Tesi, A., Abed, E. H., Genesio, R. & Wang, H. O. [1996] "Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics," Automatica 32, 1255-1271.
    • (1996) Automatica , vol.32 , pp. 1255-1271
    • Tesi, A.1    Abed, E.H.2    Genesio, R.3    Wang, H.O.4
  • 21
    • 0004596311 scopus 로고    scopus 로고
    • The Rössler equations revisited in terms of feedback circuits
    • Thomas, R. [1999a] "The Rössler equations revisited in terms of feedback circuits," J. Biol. Syst. 7, 225-237.
    • (1999) J. Biol. Syst. , vol.7 , pp. 225-237
    • Thomas, R.1
  • 22
    • 0007678353 scopus 로고    scopus 로고
    • Deterministic chaos seen in terms of feedback circuits: Analysis, synthesis, 'Labyrinth Chaos'
    • Thomas, R. [1999b] "Deterministic chaos seen in terms of feedback circuits: Analysis, synthesis, 'Labyrinth Chaos'," Int. J. Bifurcation and Chaos 9, 1889-1905.
    • (1999) Int. J. Bifurcation and Chaos , vol.9 , pp. 1889-1905
    • Thomas, R.1
  • 23
    • 0037107617 scopus 로고    scopus 로고
    • Computing accurate Poincaré maps
    • Tucker, W. [2002] "Computing accurate Poincaré maps," Physica D171, 127-137.
    • (2002) Physica , vol.D171 , pp. 127-137
    • Tucker, W.1
  • 24
    • 0035441082 scopus 로고    scopus 로고
    • The Lindstedt-Poincaré technique as an algorithm for computing periodic orbits
    • Viswanath, D. [2001] "The Lindstedt-Poincaré technique as an algorithm for computing periodic orbits," SIAM Rev. 43, 478-495.
    • (2001) SIAM Rev. , vol.43 , pp. 478-495
    • Viswanath, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.