New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems

Mechanics Research Communications

Volumn 25, Issue 1, 1998, Pages 49-58

  Belhaq, M ^a  

^a FACULTÉ DES SCIENCES AIN CHOCK   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DYNAMICS; LINEARIZATION; VECTORS;

HOMOCLINIC BIFURCATIONS; PERIODIC ORBIT; SADDLE POINT; TRIGONOMETRIC FUNCTIONS;

MATHEMATICAL TECHNIQUES;

EID: 0031641859     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0093-6413(98)00006-8     Document Type: Article

References (11)

1. SEYDEL, R., From equilibrium to chaos: Practical bifurcation and stability analysis, Elsevier, New York (1988).
2. SHILNIKOV, L. P., Some cases of generation of periodic motions in n-dimensional space. Soviet Math. Dokl. 3 (1962), 394-397.
3. ANDRONOV, A. A., LEONTOVICH, E. A., GORDON, I. I. and MAIER, A. G., Theory of bifurcations of dynamical systems on a plane. Israel Program of Scientific Translations, Jerusalem (1971).
4. MELNIKOV, V. K., On the stability of the center for time periodic perturbations. Trans. Moscow Math. Soc. 12 (1963), 1-57.
5. DOELMAN, A. and VERHULST, F., Bifurcations of strongly nonlinear self-excited oscillations", Preprint (1992).
6. GUCKENHEIMER, J. and HOLMES, P. J., Nonlinear oscillations, dynamical systems and bifurcation of vector fields. Springer-Verlag in Appl. Math. Sciences 42, , New York (1983).
7. BELHAQ, M. and FAHSI, A., Homoclinic bifurcations in self-excited oscillators. Mech. Res. Comm. 23 (1996) 4, 381-386.
8. BOGOLIOUBOV, N. and MITROPOLSKY, I., Les méthodes asymptotiques en théorie des oscillations non linéaires. Gauthier-Villars, Paris (1962).
9. BELHAQ, M., CLERC, R. L. and HARTMANN, C., Bifurcations homocliniques pour des équations de Liénard forcées périodiquement. Journal de Mécanique Théorique et Appliquée, 6 (1987) 6, 865-877.
10. BELHAQ, M. and FAHSI, A., Repeated resonances to chaos in forced oscillators. Mech. Res. Comm. 21 (1994) 5, 415-422.
11. NAYFEH, A. H. and MOOK, D. T., Nonlinear oscillations, Wiley, New York (1979).