2:2:1 resonance in the quasiperiodic Mathieu equation

Nonlinear Dynamics

Volumn 31, Issue 4, 2003, Pages 367-374

  Rand, Richard ^a   Guennoun, Kamar ^b   Belhaq, Mohamed ^b  

^a Department of Obstetrics Gynecology   (United States)

^b FACULTÉ DES SCIENCES AIN CHOCK   (Morocco)

Author keywords

Mathieu; Quasiperiodic; Resonance; Subharmonic

Indexed keywords

LYAPUNOV METHODS; PERTURBATION TECHNIQUES; RESONANCE;

MATHIEU EQUATION;

NONLINEAR EQUATIONS;

EID: 0038003833     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023216817293     Document Type: Article

References (11)

1. Rand, R., Zounes, R., and Hastings, R., 'Dynamics of a quasiperiodically forced Mathieu oscillator', in Non-Linear Dynamics: The Richard Rand 50th Anniversary Volume, A. Guran (ed.), World Scientific, Singapore, 1997, pp. 203-221.
2. Zounes, R. and Rand, R., 'Transition curves for the quasiperiodic Mathieu equation', SIAM Journal on Applied Mathematics 58, 1998, 1094-1115.
3. Zounes, R. and Rand, R., 'Global behavior of a nonlinear quasiperiodic Mathieu equation', Nonlinear Dynamics 27, 2002, 87-105.
4. Belhaq, M., Guennoun, K., and Houssni, M., 'Asymptotic solutions for a damped non-linear quasi-periodic Mathieu equation', International Journal of Non-Linear Mechanics 37, 2002, 445-460.
5. Guennoun, K., Houssni, M., and Belhaq, M., 'Quasi-periodic solutions and stability for a weakly damped nonlinear quasiperiodic Mathieu equation', Nonlinear Dynamics 27, 2002, 211-236.
6. Chirikov, B. V., 'A universal instability of many-dimensional oscillator systems', Physics Reports 52, 1979, 263-379.
7. Zounes, R. and Rand, R., 'Subharmonic resonance in the nonlinear Mathieu equation', International Journal of Non-Linear Mechanics 37, 2002, 43-73.
8. Belhaq, M. and Houssni, M., 'Quasiperiodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations', Nonlinear Dynamics 18, 1999, 1-24.
9. Zounes, R., 'An analysis of the nonlinear quasiperiodic Mathieu equation', Ph.D. Dissertation, Center for Applied Mathematics, Cornell University, Ithaca, NY, 1997.
10. Bender, C. M. and Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
11. Stoker, J. J., Nonlinear Vibrations in Mechanical and Electrical Systems, Wiley, New York, 1950.