Asymptotic analysis of autoresonance models

L. A. Kalyakin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 5, pp. 791-857

Résumé

In recent decades new problems have arisen in oscillation theory which are related to the investigation of a physical phenomenon known as autoresonance. This paper presents a survey of results on the asymptotic analysis of such problems. Systems of differential equations corresponding to non-linear non-autonomous oscillators with variable excitation frequency are considered. For their solution asymptotic formulae are constructed with respect to a small parameter or with respect to an independent variable.

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