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Volumn 23, Issue 1, 2000, Pages 67-86

Homoclinic connections in strongly self-excited nonlinear oscillators: The melnikov function and the elliptic lindstedt-poincaré method

Author keywords

Elliptic lindstedt poincar method; Homoclinic bifurcations criteria; Melnikov function

Indexed keywords


EID: 0013027015     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008316010341     Document Type: Article
Times cited : (53)

References (34)
  • 9
    • 0014719916 scopus 로고
    • Approximate solutions of non-linear non-autonomous second-order differential equations
    • Barkham, P. G. D. and Soudack, A. C., 'Approximate solutions of non-linear non-autonomous second-order differential equations', International Journal of Control 11, 1970, 101-114.
    • (1970) International Journal of Control , vol.11 , pp. 101-114
    • Barkham, P.G.D.1    Soudack, A.C.2
  • 10
    • 0014872494 scopus 로고
    • Further results on approximate solutions of non-linear, non-autonomous second-order differential equations
    • Soudack, A. C. and Barkham, P. G. D., 'Further results on approximate solutions of non-linear, non-autonomous second-order differential equations', International Journal of Control 12, 1970, 763-767.
    • (1970) International Journal of Control , vol.12 , pp. 763-767
    • Soudack, A.C.1    Barkham, P.G.D.2
  • 11
    • 0038484459 scopus 로고
    • On the transient solution of the unforced Duffing equation with large damping
    • Soudack, A. C. and Barkham, P. G. D., 'On the transient solution of the unforced Duffing equation with large damping', International Journal of Control 13, 1971, 767-769.
    • (1971) International Journal of Control , vol.13 , pp. 767-769
    • Soudack, A.C.1    Barkham, P.G.D.2
  • 12
    • 0024648820 scopus 로고
    • Extension and improvement to the Krylov-Bogolioubov methods using elliptic functions
    • Yuste, S. B. and Bejarano, J. D., 'Extension and improvement to the Krylov-Bogolioubov methods using elliptic functions', International Journal of Control 49, 1989, 1127-1141.
    • (1989) International Journal of Control , vol.49 , pp. 1127-1141
    • Yuste, S.B.1    Bejarano, J.D.2
  • 14
    • 0023647910 scopus 로고
    • Amplitude decay of damped non-linear oscillators studied with Jacobian elliptic functions
    • Yuste, S. B. and Bejarano, J. D., 'Amplitude decay of damped non-linear oscillators studied with Jacobian elliptic functions', Journal of Sound and Vibration 114, 1987, 33-44.
    • (1987) Journal of Sound and Vibration , vol.114 , pp. 33-44
    • Yuste, S.B.1    Bejarano, J.D.2
  • 15
    • 0025546248 scopus 로고
    • Using computer algebra to handle elliptic functions in the method of averaging
    • American Society Mechanical Engineers PVP, ASME, New York
    • Rand, R. H., 'Using computer algebra to handle elliptic functions in the method of averaging', in Symbolic Computations and Their Impact on Dynamics, American Society Mechanical Engineers PVP, Vol. 205, ASME, New York, 1990, pp. 311-326.
    • (1990) Symbolic Computations and Their Impact on Dynamics , vol.205 , pp. 311-326
    • Rand, R.H.1
  • 16
    • 0022790036 scopus 로고
    • Construction of approximate analytical solutions to a new class of nonlinear oscillator equations
    • Yuste, S. B. and Bejarano, J. D., 'Construction of approximate analytical solutions to a new class of nonlinear oscillator equations', Journal of Sound and Vibration 110, 1986, 347-350.
    • (1986) Journal of Sound and Vibration , vol.110 , pp. 347-350
    • Yuste, S.B.1    Bejarano, J.D.2
  • 17
    • 0343600055 scopus 로고
    • Generalized Fourier series and limit cycles of generalized van der Pol oscillators
    • Garcia-Margallo, J. and Bejarano, J. D., 'Generalized Fourier series and limit cycles of generalized van der Pol oscillators', International Journal of Control 49, 1988, 1127-1141.
    • (1988) International Journal of Control , vol.49 , pp. 1127-1141
    • Garcia-Margallo, J.1    Bejarano, J.D.2
  • 18
    • 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
  • 19
    • 0342295127 scopus 로고
    • Macsyma program to implement averaging using elliptic functions
    • K. R. Meyer and D. S. Schmidt (eds.), Springer-Verlag, Berlin
    • 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, Berlin, 1991, pp. 71-89.
    • (1991) Computer Aided Proofs in Analysis , pp. 71-89
    • Coppola, V.T.1    Rand, R.H.2
  • 20
    • 0031095817 scopus 로고    scopus 로고
    • An elliptic Lindstedt-Poincaré method for certain strongly non-linear oscillators
    • Chen, S. H. and Cheung, Y. K., 'An elliptic Lindstedt-Poincaré method for certain strongly non-linear oscillators', Nonlinear Dynamics 12, 1997, 199-213.
    • (1997) Nonlinear Dynamics , vol.12 , pp. 199-213
    • Chen, S.H.1    Cheung, Y.K.2
  • 21
    • 0030195763 scopus 로고    scopus 로고
    • New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems
    • Belhaq, M., 'New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems', Mechanics Research Communications 23(4), 1998, 381-386.
    • (1998) Mechanics Research Communications , vol.23 , Issue.4 , pp. 381-386
    • Belhaq, M.1
  • 22
    • 0032641070 scopus 로고    scopus 로고
    • Predicting homoclinic bifurcations in planar autonomous systems
    • Belhaq, M., Lakrad, F., and Fahsi, A., 'Predicting homoclinic bifurcations in planar autonomous systems', Nonlinear Dynamics 18(4), 1999, 303-310.
    • (1999) Nonlinear Dynamics , vol.18 , Issue.4 , pp. 303-310
    • Belhaq, M.1    Lakrad, F.2    Fahsi, A.3
  • 23
    • 0030195763 scopus 로고    scopus 로고
    • Homoclinic bifurcations in self-excited oscillators
    • Belhaq, M. and Fahsi, A., 'Homoclinic bifurcations in self-excited oscillators', Mechanics Research Communications 23(4), 1996, 381-386.
    • (1996) Mechanics Research Communications , vol.23 , Issue.4 , pp. 381-386
    • Belhaq, M.1    Fahsi, A.2
  • 24
    • 0030285349 scopus 로고    scopus 로고
    • Separatrices and limit cycles of strongly nonlinear oscillators by the perturbation-incremental method
    • Xu, Z., Chen, H. S. Y., and Chung, K. W., 'Separatrices and limit cycles of strongly nonlinear oscillators by the perturbation-incremental method', Nonlinear Dynamics 11, 1996, 213-233.
    • (1996) Nonlinear Dynamics , vol.11 , pp. 213-233
    • Xu, Z.1    Chen, H.S.Y.2    Chung, K.W.3
  • 27
    • 0029691221 scopus 로고    scopus 로고
    • Discretization of homoclinic orbits and invisible chaos
    • American Mathematical Society, Providence, RI
    • Fiedler, B. and Scheurle, J., 'Discretization of homoclinic orbits and invisible chaos', in Memoirs of American Mathematical Society, Vol. 570, American Mathematical Society, Providence, RI, 1996.
    • (1996) Memoirs of American Mathematical Society , vol.570
    • Fiedler, B.1    Scheurle, J.2
  • 28
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer, K. J., 1984, 'Exponential dichotomies and transversal homoclinic points', Journal of Differential Equations 55, 1984, 225-256.
    • (1984) Journal of Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 31
    • 84974232147 scopus 로고
    • Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. the cusp case of codimension 3
    • Dumortier, F., Roussarie, R., and Sotomayor, J., 'Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3', 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.