2:1:1 Resonance in the quasi-periodic mathieu equation

Nonlinear Dynamics

Volumn 40, Issue 2, 2005, Pages 195-203

  Rand, Richard ^a   Morrison, Tina ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Parametric excitation; Quasi periodic Mathieu equation; Resonance

Indexed keywords

APPROXIMATION THEORY; INTEGRATION; NUMERICAL METHODS; PERTURBATION TECHNIQUES; RESONANCE; SET THEORY;

NUMERICAL INTEGRATION OF EQUATION; PARAMETRIC EXCITATION; QUASI-PERIODIC MATHIEU EQUATION; TRANSITION CURVES;

DYNAMICS;

EID: 17144390773     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-005-6005-8     Document Type: Article

References (8)

1. Zounes, R. S. and Rand, R. H., 'Transition curves in the quasi-periodic Mathieu equation', SIAM Journal of Applied Mathematics 58, 1998, 1094-1115.
2. Rand, R., Zounes, R., and Hastings, R., 'A quasi-periodic Mathieu equation', Chap. 9, In Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume, A. Guran (ed.), World Scientific Publications, 1997, pp. 203-221.
3. Mason, S. and Rand, R., 'On the torus flow Y' = A + B COS Y + C COS X and its relation to the quasi-periodic Mathieu equation', in Proceedings of the 1999 ASME Design Engineering Technical Conferences, Las Vegas, NV, September 12-15, 1999, Paper no. DETC99/VIB-8052 (CD-ROM).
4. Zounes, R. S. and Rand, R. H., 'Global behavior of a nonlinear quasi-periodic Mathieu equation', Nonlinear Dynamics 27, 2002, 87-105.
5. Rand, R., Guennoun, K., and Belhaq, M., '2:2:1 Resonance in the quasi-periodic Mathieu equation', Nonlinear Dynamics 31, 2003, 367-374.
6. Guennoun, K., Houssni, M., and Belhaq, M., 'Quasi-periodic solutions and stability for a weakly damped nonlinear quasi-periodic Mathieu equation', Nonlinear Dynamics 27, 2002, 211-236.
7. 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.
8. Rand, R. H., Lecture Notes on Nonlinear Vibrations (version 45), Published on-line by The Internet-First University Press, Ithaca, NY, 004, http://dspace.library.cornell.edu/handle/1813/79.