Relaxation oscillations of a van der Pol equation with large critical forcing term
- 1 January 1980
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 38 (1), 9-16
- https://doi.org/10.1090/qam/575829
Abstract
A van der Pol equation with sinusoidal forcing term is analyzed with singular perturbation methods for large values of the parameter. Asymptotic approximations of (sub)harmonic solutions with period T = 2 π ( 2 n − 1 ) , n = 1 , 2 , . . . T = 2\pi \left ( {2n - 1} \right ),n = 1, 2, ... are constructed under certain restricting conditions for the amplitude of the forcing term. These conditions are such that always two solutions with period T = 2 π ( 2 n ± 1 ) T = 2\pi \left ( {2n \pm 1} \right ) coexist.Keywords
This publication has 9 references indexed in Scilit:
- A Course of Modern AnalysisPublished by Cambridge University Press (CUP) ,1996
- Qualitative analysis of the periodically forced relaxation oscillationsMemoirs of the American Mathematical Society, 1981
- Symbolic dynamics and relaxation oscillationsPhysica D: Nonlinear Phenomena, 1980
- Frequency Entrainment of a Forced van der Pol OscillatorStudies in Applied Mathematics, 1978
- Asymptotic Methods for Relaxation OscillationsNorth-Holland Mathematics Studies, 1978
- Relaxation Oscillations Governed by a Van der Pol Equation with Periodic Forcing TermSIAM Journal on Applied Mathematics, 1976
- The method of matched asymptotic expansions for the periodic solution of the van der pol equationInternational Journal of Non-Linear Mechanics, 1974
- On the non-autonomous van der Pol equation with large parameterMathematical Proceedings of the Cambridge Philosophical Society, 1972
- A Second Order Differential Equation with Singular SolutionsAnnals of Mathematics, 1949