Relaxation Oscillations Governed by a Van der Pol Equation with Periodic Forcing Term

J. Grasman, E. J. M. Veling, George M. Willems

Type: Article

Publication Date: 1976-12-01

Citations: 33

DOI: https://doi.org/10.1137/0131059

Abstract

A Van der Pol equation with periodic forcing term is investigated for large values of the parameter. A synchronized periodic solution is approximated by singular perturbation methods. It appears that the parameter $\nu $ and the amplitude b of the forcing term have to satisfy certain conditions for finding a matched asymptotic approximation. In the b, $\nu $-plane overlapping regions are constructed in which these conditions are satisfied. In the domain of overlap two periodic solutions with different periods are possible which is in agreement with numerical and analytical results.

Locations

CWI's Institutional Repository (Centrum Wiskunde & Informatica) - View - PDF
SIAM Journal on Applied Mathematics - View

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+	Asymptotic Methods in the Theory of Nonlinear Oscillations	1961	N. N. Bogolyubov Yu. A. Mitropol’skii
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