Relaxation oscillations of a van der Pol equation with large critical forcing term

Grasman, J.

doi:10.1090/qam/575829

Author: J. Grasman
Journal: Quart. Appl. Math. 38 (1980), 9-16
MSC: Primary 70K99; Secondary 34D15, 58F22
DOI: https://doi.org/10.1090/qam/575829
MathSciNet review: 575829
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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 $T = 2\pi \left ( {2n - 1} \right ),n = 1, 2, ...$ are constructed under certain restricting conditions for the amplitude of the forcing term. These conditions are such that always two solutions with period $T = 2\pi \left ( {2n \pm 1} \right )$ coexist.

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