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
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