Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T20:12:34.372Z Has data issue: false hasContentIssue false

On relaxation oscillations in a forced van der Pol oscillator

Published online by Cambridge University Press:  14 November 2011

P. Habets
Affiliation:
Université Catholique de Louvain

Synopsis

Relaxation oscillations of a forced van der Pol oscillator are considered. The limiting behaviour of such a solution is investigated using a priori estimates. This simplifies previous approaches of the problem.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Berger, M. and Berger, M.. Perspectives in nonlinearity. An introduction to nonlinear analysis. (New York: W. A. Benjamin, 1968).Google Scholar
2Cartwright, M. L. and Littlewood, J. E.. On nonlinear differential equations of the second order I. J. London Math. Soc. 20 (1945), 180189.CrossRefGoogle Scholar
3Levinson, N.. Perturbation of discontinuous solutions of nonlinear system of differential equations. Acta. Math. 82 (1950), 71106.CrossRefGoogle Scholar
4Lloyd, N. G.. On the non-autonomous van der Pol equation with large parameter. Math. Proc. Cambridge Philos. Soc. 72 (1972), 213227.CrossRefGoogle Scholar
5Sibuya, Y.. On perturbations of discontinuous solutions of ordinary differential equations. Natur. Sci. Rep. Ochanomizu Univ. 11 (1960), 118.Google Scholar
6Rouche, N. and Mawhin, J.. Equations différentielles ordinaires (Paris: Masson, 1973).Google Scholar
7Wendel, J. G.. Singular perturbations of a van der Pol equation. Contributions to the Theory of Nonlinear Oscillations. Annals of Mathematics Studies, 20, 243290 (Princeton: University Press, 1950).Google Scholar