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Volumn 14, Issue 8, 2004, Pages 2753-2775

Global dynamics of a duffing oscillator with delayed displacement feedback

Author keywords

Basin of attraction; Chaos; Hopf bifurcation; Periodicity in delay; Stability switch; Time delay

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; COMPUTATIONAL METHODS; DELAY CIRCUITS; FEEDBACK; MATHEMATICAL MODELS; TOPOLOGY;

EID: 4944245946     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404010990     Document Type: Article
Times cited : (55)

References (35)
  • 1
    • 0042148724 scopus 로고    scopus 로고
    • Tool to recover scalar time-delay systems form experimental time series
    • Bünner, M. J., Popp, M., Meyer, Th., Kittel, A. & Parisi, J. [1996] "Tool to recover scalar time-delay systems form experimental time series," Phys. Rev. E54, R3082-R3085
    • (1996) Phys. Rev. E , vol.54
    • Bünner, M.J.1    Popp, M.2    Meyer, T.3    Kittel, A.4    Parisi, J.5
  • 2
    • 0000768778 scopus 로고    scopus 로고
    • Recovery of the time-evolution equation of time delay systems from time series
    • . Bünner, M. J., Meyer, Th., Kittel, A. & Parisi, J. [1997] "Recovery of the time-evolution equation of time delay systems from time series," Phys. Rev. E56, 5083-5089.
    • (1997) Phys. Rev. , vol.E56 , pp. 5083-5089
    • Bünner, M.J.1    Meyer, T.2    Kittel, A.3    Parisi, J.4
  • 3
    • 0000109792 scopus 로고    scopus 로고
    • Resonant codimension two bifurcation in the harmonic oscillator with delayed forcing
    • Campbell, S. A. & Bélair, J. [1999] "Resonant codimension two bifurcation in the harmonic oscillator with delayed forcing," Canad. Appl. Math. Quart. 7, 217-238.
    • (1999) Canad. Appl. Math. Quart. , vol.7 , pp. 217-238
    • Campbell, S.A.1    Bélair, J.2
  • 4
    • 0019070376 scopus 로고
    • A Poincaré-Lindstedt approach to bifurcation problems for differential-delay equations
    • Casal, A. & Freedman, M. [1980] "A Poincaré-Lindstedt approach to bifurcation problems for differential-delay equations," IEEE Trans. Auto. Cont. AC-25, 967-973.
    • (1980) IEEE Trans. Auto. Cont. , vol.AC-25 , pp. 967-973
    • Casal, A.1    Freedman, M.2
  • 6
    • 0000840164 scopus 로고
    • Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
    • Faria, F. L. & Magalhaes, T. [1995] "Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation," J. Diff. Eqs. 122, 181-200.
    • (1995) J. Diff. Eqs. , vol.122 , pp. 181-200
    • Faria, F.L.1    Magalhaes, T.2
  • 7
    • 0042302880 scopus 로고
    • Periodic solutions of certain Liennard equations with delay
    • Grafton, R. [1972] "Periodic solutions of certain Liennard equations with delay," J. Diff. Eqs. 11, 519-527.
    • (1972) J. Diff. Eqs. , vol.11 , pp. 519-527
    • Grafton, R.1
  • 9
    • 0016027034 scopus 로고
    • A theory of non-linear regenerative chatter
    • Hanna, N. H. & Tobias, S. A. [1974] "A theory of non-linear regenerative chatter," ASME Trans. J. Eng. Industry 96, 247-255.
    • (1974) Asme Trans. J. Eng. Industry , vol.96 , pp. 247-255
    • Hanna, N.H.1    Tobias, S.A.2
  • 11
    • 0001114217 scopus 로고    scopus 로고
    • Counting roots of the characteristic equation for linear-delay differential systems
    • Hassard, B. D. [1997] "Counting roots of the characteristic equation for linear-delay differential systems," J. Diff. Eqs. 136, 222-235.
    • (1997) J. Diff. Eqs. , vol.136 , pp. 222-235
    • Hassard, B.D.1
  • 12
    • 0001009039 scopus 로고
    • Existence of chaos in control system with delayed feedback
    • Heiden, U. van der & Walther, H. O. [1983] "Existence of chaos in control system with delayed feedback," J. Diff. Eqs. 47, 273-295.
    • (1983) J. Diff. Eqs. , vol.47 , pp. 273-295
    • Van Der, H.U.1    Walther, H.O.2
  • 13
    • 0032048711 scopus 로고    scopus 로고
    • Resonances of a harmonically forced Duffing oscillator with time delay state feedback
    • Hu, H. Y., Dowell, E. H. & Virgin, L. N. [1998] "Resonances of a harmonically forced Duffing oscillator with time delay state feedback," Nonlin. Dyn. 15, 311-327.
    • (1998) Nonlin. Dyn. , vol.15 , pp. 311-327
    • Hu, H.Y.1    Dowell, E.H.2    Virgin, L.N.3
  • 14
    • 0842270521 scopus 로고    scopus 로고
    • Abundant dynamic features of a non-linear system under delayed feedback control
    • Hu, H. Y. [2001] "Abundant dynamic features of a non-linear system under delayed feedback control," in Proc. 6th Asia-Pacific Vibration Conf. 1, pp. 11-15.
    • (2001) Proc. 6th Asia-Pacific Vibration Conf. , vol.1 , pp. 11-15
    • Hu, H.Y.1
  • 17
    • 0032622601 scopus 로고    scopus 로고
    • Experimental characterization of quasi-periodicity and chaos in a mechanical system with delay
    • Johnson, M. A. & Moon, F. C. [1999] "Experimental characterization of quasi-periodicity and chaos in a mechanical system with delay," Int. J. Bifurcation and Chaos 9, 49-65.
    • (1999) Int. J. Bifurcation and Chaos , vol.9 , pp. 49-65
    • Johnson, M.A.1    Moon, F.C.2
  • 19
    • 0035622326 scopus 로고    scopus 로고
    • Local stability, Hopf and resonant codimension-two bifurcation in a harmonic oscillator with two time delays
    • Liao, X. F. & Chen, G. R. [2001] "Local stability, Hopf and resonant codimension-two bifurcation in a harmonic oscillator with two time delays," Int. J. Bifurcation and Chaos 11, 2105-2121.
    • (2001) Int. J. Bifurcation and Chaos , vol.11 , pp. 2105-2121
    • Liao, X.F.1    Chen, G.R.2
  • 20
    • 0029546791 scopus 로고
    • Hopf bifurcations in time-delayed nonlinear feedback control systems
    • Moiola, J. L. & Chen, G. R. [1995] "Hopf bifurcations in time-delayed nonlinear feedback control systems," in Proc. 34th Conf. Decision and Control, pp. 942-948.
    • (1995) Proc. 34th Conf. Decision and Control , pp. 942-948
    • Moiola, J.L.1    Chen, G.R.2
  • 21
    • 0019064545 scopus 로고
    • Experiments on chaotic motions of a forced nonlinear oscillator: Strange attractors
    • Moon, F. C. [1980] "Experiments on chaotic motions of a forced nonlinear oscillator: Strange attractors," ASME Trans. J. Appl. Mech. 47, 638-644.
    • (1980) ASME Trans. J. Appl. Mech. , vol.47 , pp. 638-644
    • Moon, F.C.1
  • 23
    • 0010206984 scopus 로고
    • A perturbative approach to periodic solutions of delay differential equation
    • Morris, H. C. [1976] "A perturbative approach to periodic solutions of delay differential equation," J. Inst. Math. Appl. 18, 15-24.
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 15-24
    • Morris, H.C.1
  • 24
    • 0002787211 scopus 로고    scopus 로고
    • Applications of perturbation methods to tool chatter dynamics
    • ed. Moon, F. C. (John Wiley)
    • Nayfeh, A., Chin, C. & Pratt, J. [1997] "Applications of perturbation methods to tool chatter dynamics," in Dynamics and Chaos in Manufacturing Processes, ed. Moon, F. C. (John Wiley), pp. 193-213.
    • (1997) Dynamics and Chaos in Manufacturing Processes , pp. 193-213
    • Nayfeh, A.1    Chin, C.2    Pratt, J.3
  • 25
    • 0023419943 scopus 로고
    • Nonlinear structural vibrations involving a time delay in damping
    • Plaut, R. H. & Hsieh, J. C. [1987] "Nonlinear structural vibrations involving a time delay in damping," J. Sound Vibr. 117, 497-510.
    • (1987) J. Sound Vibr. , vol.117 , pp. 497-510
    • Plaut, R.H.1    Hsieh, J.C.2
  • 27
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation, and multi-stability in a system of two coupled neurones with multiple time delays
    • Shayer, L. & Campbell, S. A. [2000] "Stability, bifurcation, and multi-stability in a system of two coupled neurones with multiple time delays," SIAM J. Appl. Math. 61, 673-700.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 673-700
    • Shayer, L.1    Campbell, S.A.2
  • 29
    • 0029486988 scopus 로고
    • Quasi-periodic oscillations in a robot dynamics
    • Stépán, G. & Haller, G. [1995] "Quasi-periodic oscillations in a robot dynamics," Nonlin. Dyn. 8, 513-528.
    • (1995) Nonlin. Dyn. , vol.8 , pp. 513-528
    • Stépán, G.1    Haller, G.2
  • 30
    • 0842313698 scopus 로고    scopus 로고
    • Modelling nonlinear regenrerative effects in metal cutting
    • Stépán, G. [2000] "Modelling nonlinear regenrerative effects in metal cutting," Phil. Trans. R. Soc. Lond. A359, 739-757.
    • (2000) Phil. Trans. R. Soc. Lond. , vol.A359 , pp. 739-757
    • Stépán, G.1
  • 31
    • 7944221027 scopus 로고    scopus 로고
    • Hopf-bifurcation of an oscillator with quadratic and cubic nonlinearities and with delayed velocity feedback
    • in press
    • Wang, H. L., Wang, Z. H. & Hu, H. Y. [2004] "Hopf-bifurcation of an oscillator with quadratic and cubic nonlinearities and with delayed velocity feedback," Acta Mech. Sin. 4, in press.
    • (2004) Acta Mech. Sin. , vol.4
    • Wang, H.L.1    Wang, Z.H.2    Hu, H.Y.3
  • 32
    • 0007790565 scopus 로고    scopus 로고
    • Delay-independent stability of retarded dynamic systems of multiple degrees of freedom
    • Wang, Z. H. & Hu, H. Y. [1999] "Delay-independent stability of retarded dynamic systems of multiple degrees of freedom," J. Sound Vibr. 226, 57-81.
    • (1999) J. Sound Vibr. , vol.226 , pp. 57-81
    • Wang, Z.H.1    Hu, H.Y.2
  • 33
    • 0033682963 scopus 로고    scopus 로고
    • Stability switches of time-delayed dynamic systems with unknown parameters
    • Wang, Z. H. & Hu, H. Y. [2000] "Stability switches of time-delayed dynamic systems with unknown parameters," J. Sound Vibr. 233, 215-233.
    • (2000) J. Sound Vibr. , vol.233 , pp. 215-233
    • Wang, Z.H.1    Hu, H.Y.2
  • 34
    • 0031100897 scopus 로고    scopus 로고
    • Bifurcation control of parametrically excited Duffing system by a combined linear-plus-nonlinear feedback control
    • Yabuno, H. [1997] "Bifurcation control of parametrically excited Duffing system by a combined linear-plus-nonlinear feedback control," Nonlin. Dyn. 12, 263-274.
    • (1997) Nonlin. Dyn. , vol.12 , pp. 263-274
    • Yabuno, H.1
  • 35
    • 0043179007 scopus 로고    scopus 로고
    • Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback
    • Yu, P., Yuan, Y. & Xu, J. [2002] "Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback," Commun. Nonlin. Sci. Numer. Simul. 7, 69-91.
    • (2002) Commun. Nonlin. Sci. Numer. Simul. , vol.7 , pp. 69-91
    • Yu, P.1    Yuan, Y.2    Xu, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.