The multiple scales method, homoclinic bifurcation and Melnikov's method for autonomous systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 11, 1998, Pages 2099-2105

  Smith, Peter ^a  

^a KEELE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032214547     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812749800173X     Document Type: Article

References (13)

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3. Drazin, P. G. [1992] Nonlinear Systems (Cambridge University Press).
4. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
5. Hartman, P. [1964] Ordinary Differential Equations (Wiley, NY).
6. Holmes, P. J. [1980] "Averaging and chaotic motions in forced oscillations," SIAM J. Appl. Math. 38, 65-80.
7. Jordan, D. W. & Smith, P. [1987] Nonlinear Ordinary Differential Equations, 2nd edition (Oxford University Press).
8. Kevorkian, J. & Cole, J. D. [1996] Multiple Scales and Singular Perturbation Methods (Springer-Verlag, NY).
9. Melnikov, V. K. [1963] "On the stability of the center for time periodic perturbations," Trans. Moscow Math. Soc. 12, 1-57.
10. Nayfeh, A. H. & Balachandran, B. [1995] Applied Nonlinear Dynamics (Wiley, NY).
11. Sanders, J. A. [1982] "Melnikov's method and averaging," Celestial Mechanics 28, 171-181.
12. Smith, P. & Yorke, J. M. E. [1992] "A dual perturbation series analysis of homoclinic bifurcation for autonomous systems," Z. Angew. Math. Mech. 72, 269-275.
13. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, NY).