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Volumn 231, Issue 1, 2000, Pages 145-173

Study of the limit cycles associated with a generalized codimension-3 Lienard oscillator

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DAMPING; DEGREES OF FREEDOM (MECHANICS); MACHINE TOOLS; MACHINE VIBRATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; OSCILLATIONS;

EID: 0033734895     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1999.2673     Document Type: Article
Times cited : (25)

References (36)
  • 1
    • 0004068151 scopus 로고    scopus 로고
    • Nonlinear dynamics and chaos in manufacturing processes
    • MOON F. C. New York: John Wiley & Sons
    • MOON F. C., JOHNSON M. A. Nonlinear dynamics and chaos in manufacturing processes. MOON F. C. Dynamics and Chaos in Manufacturing Processes. 1998;3-32 John Wiley & Sons, New York.
    • (1998) Dynamics and Chaos in Manufacturing Processes , pp. 3-32
    • Moon, F.C.1    Johnson, M.A.2
  • 2
    • 38249030272 scopus 로고
    • A model of the combined effects of vortex-induced vibration and galloping
    • CORLESS R. M., PARKINSON G. V. A model of the combined effects of vortex-induced vibration and galloping. Journal of Fluids and Structures. 2:1988;203-220.
    • (1988) Journal of Fluids and Structures , vol.2 , pp. 203-220
    • Corless, R.M.1    Parkinson, G.V.2
  • 3
    • 0027458271 scopus 로고
    • A model of the combined effects of vortex-induced vibration and galloping Part II
    • CORLESS R. M., PARKINSON G. V. A model of the combined effects of vortex-induced vibration and galloping Part II. Journal of Fluids and Structures. 7:1993;825-848.
    • (1993) Journal of Fluids and Structures , vol.7 , pp. 825-848
    • Corless, R.M.1    Parkinson, G.V.2
  • 8
    • 0024964232 scopus 로고
    • An approach to study the effects of tool geometry on the primary chatter vibration in orthogonal cutting
    • HAMDAN M. N., BAYOUMI A. E. An approach to study the effects of tool geometry on the primary chatter vibration in orthogonal cutting. Journal of Sound and Vibration. 128:1989;451-469.
    • (1989) Journal of Sound and Vibration , vol.128 , pp. 451-469
    • Hamdan, M.N.1    Bayoumi, A.E.2
  • 11
    • 0001720655 scopus 로고    scopus 로고
    • Number of limit cycles of the Lienard equation
    • GIACOMINI H., NEUKIRCH S. Number of limit cycles of the Lienard equation. Physical Review E. 56:1997;3809-3813.
    • (1997) Physical Review e , vol.56 , pp. 3809-3813
    • Giacomini, H.1    Neukirch, S.2
  • 12
    • 4244172969 scopus 로고    scopus 로고
    • Lienard systems, limit cycles, and Melnikov theory
    • SANJUAN M. A. F. Lienard systems, limit cycles, and Melnikov theory. Physical Review E. 57:1998;340-344.
    • (1998) Physical Review e , vol.57 , pp. 340-344
    • Sanjuan, M.A.F.1
  • 13
    • 0032487706 scopus 로고
    • Lienard systems, limit cycles, Melnikov theory, and the method of slowly varying amplitude and phase
    • MICKENS R. E. Lienard systems, limit cycles, Melnikov theory, and the method of slowly varying amplitude and phase. Journal of Sound and Vibration. 217:1988;790-793.
    • (1988) Journal of Sound and Vibration , vol.217 , pp. 790-793
    • Mickens, R.E.1
  • 14
    • 0042071548 scopus 로고
    • The number of limit cycles for the generalized mixed Rayleigh-Lienard oscillator
    • BURNETTE J., MICKENS R. E. The number of limit cycles for the generalized mixed Rayleigh-Lienard oscillator. Journal of Sound and Vibration. 188:1995;298-300.
    • (1995) Journal of Sound and Vibration , vol.188 , pp. 298-300
    • Burnette, J.1    Mickens, R.E.2
  • 15
    • 0000144083 scopus 로고
    • Normal forms for certain singularities of vector fields
    • TAKENS F. Normal forms for certain singularities of vector fields. Annales de Institute Fourier. 23:1973;163-195.
    • (1973) Annales de Institute Fourier , vol.23 , pp. 163-195
    • Takens, F.1
  • 17
    • 0002533366 scopus 로고
    • Forced oscillations and bifurcations
    • TAKENS F. Forced oscillations and bifurcations. Comm. Math. Inst. 3:1974;1-59.
    • (1974) Comm. Math. Inst , vol.3 , pp. 1-59
    • Takens, F.1
  • 18
    • 34250403445 scopus 로고
    • Versal deformations of a singular point on the plane in the case of zero eigenvalues
    • BOGDANOV R. I. Versal deformations of a singular point on the plane in the case of zero eigenvalues. Functional Analysis and Its Applications. 9:1975;144-145.
    • (1975) Functional Analysis and Its Applications , vol.9 , pp. 144-145
    • Bogdanov, R.I.1
  • 19
    • 0003048025 scopus 로고
    • Bifurcations of a limit cycle for a family of vector fields on the plane (English translation: Selecta Mathematics Formerly Sovietica 1 (1981), 373-388.) (in Russian)
    • BOGDANOV R. I. Bifurcations of a limit cycle for a family of vector fields on the plane (English translation: Selecta Mathematics Formerly Sovietica 1 (1981), 373-388.) (in Russian). Proceedings of Petrovskii Seminar. 2:1976;23-35.
    • (1976) Proceedings of Petrovskii Seminar , vol.2 , pp. 23-35
    • Bogdanov, R.I.1
  • 20
    • 84974232147 scopus 로고
    • Generic 3-parameter families of vector field on the lane, unfolding a singularity with nilpotent linear part. The cusp case
    • DUMORTIER F., ROUSSARIE R., SOTOMAYOR J. Generic 3-parameter families of vector field on the lane, unfolding a singularity with nilpotent linear part. The cusp case. Ergodic Theory and Dynamical Systems. 7:1987;375-413.
    • (1987) Ergodic Theory and Dynamical Systems , vol.7 , pp. 375-413
    • Dumortier, F.1    Roussarie, R.2    Sotomayor, J.3
  • 21
    • 85007165089 scopus 로고
    • Generic 3-parameter families of planar vector fields, unfolding of saddle, focus and elliptic singularities with nilpotent linear parts
    • DUMORTIER F., ROUSSARIE R., SOTOMAYOR J. Generic 3-parameter families of planar vector fields, unfolding of saddle, focus and elliptic singularities with nilpotent linear parts. Preprint. 1990.
    • (1990) Preprint
    • Dumortier, F.1    Roussarie, R.2    Sotomayor, J.3
  • 22
    • 38249022236 scopus 로고
    • A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4
    • LI C., ROUSSEAU C. A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: the cusp of order 4. Journal of Differential Equation. 79:1989;132-167.
    • (1989) Journal of Differential Equation , vol.79 , pp. 132-167
    • Li, C.1    Rousseau, C.2
  • 23
    • 0001091813 scopus 로고
    • Codimension 2 symmetric bifurcation and application to 1:2 resonance
    • LI C., ROUSSEAU C. Codimension 2 symmetric bifurcation and application to 1:2 resonance. Canadian Journal of Mathematics. XLII:1990;191-212.
    • (1990) Canadian Journal of Mathematics , vol.42 , pp. 191-212
    • Li, C.1    Rousseau, C.2
  • 26
    • 0023167367 scopus 로고
    • On codimension-three bifurcation in the motion of articulated tubes conveying a fluid
    • SETHNA P. R., SHAW S. W. On codimension-three bifurcation in the motion of articulated tubes conveying a fluid. Physica D. 24:1987;305-327.
    • (1987) Physica D , vol.24 , pp. 305-327
    • Sethna, P.R.1    Shaw, S.W.2
  • 27
  • 28
    • 0013301865 scopus 로고
    • Normal form and codimension three degenerate bifurcations in a nonlinear dynamical system
    • ZHANG W. Normal form and codimension three degenerate bifurcations in a nonlinear dynamical system. Acta Mechanics Sinica. 25:1993;548-559.
    • (1993) Acta Mechanics Sinica , vol.25 , pp. 548-559
    • Zhang, W.1
  • 29
    • 0032435442 scopus 로고    scopus 로고
    • Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues
    • BI Q., YU P. Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues. International Journal of Bifurcations and Chaos. 8:1998;2279-2319.
    • (1998) International Journal of Bifurcations and Chaos , vol.8 , pp. 2279-2319
    • Bi, Q.1    Yu, P.2
  • 30
    • 0032487691 scopus 로고    scopus 로고
    • Analysis of non-linear dynamics and bifurcations of a double pendulum
    • YU P., BI Q. Analysis of non-linear dynamics and bifurcations of a double pendulum. Journal of Sound and Vibration. 217:1998;691-736.
    • (1998) Journal of Sound and Vibration , vol.217 , pp. 691-736
    • Yu, P.1    Bi, Q.2
  • 31
    • 49049152726 scopus 로고
    • A method of constructing cycles without contact around a weak focus
    • SHI S. L. A method of constructing cycles without contact around a weak focus. Journal of Differential Equations. 41:1981;301-312.
    • (1981) Journal of Differential Equations , vol.41 , pp. 301-312
    • Shi, S.L.1
  • 33
    • 0001799622 scopus 로고
    • Number of zeroes of complete elliptic integrals
    • PETROV G. S. Number of zeroes of complete elliptic integrals. Functional Analysis & Applications. 18:1984;148-150.
    • (1984) Functional Analysis & Applications , vol.18 , pp. 148-150
    • Petrov, G.S.1
  • 34
    • 0001888119 scopus 로고
    • Elliptic integrals and their nonoscillation
    • PETROV G. S. Elliptic integrals and their nonoscillation. Functional Analysis Applications. 20:1986;37-40.
    • (1986) Functional Analysis Applications , vol.20 , pp. 37-40
    • Petrov, G.S.1
  • 35
    • 51249177330 scopus 로고
    • Complex zeroes of an elliptic integral
    • PETROV G. S. Complex zeroes of an elliptic integral. Functional Analysis Applications. 21:1987;247-248.
    • (1987) Functional Analysis Applications , vol.21 , pp. 247-248
    • Petrov, G.S.1
  • 36


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.