Geodesic
Asymptotic analysis of autoresonance models
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 5, pp. 791-857

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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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     author = {L. A. Kalyakin},
     title = {Asymptotic analysis of autoresonance models},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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L. A. Kalyakin. Asymptotic analysis of autoresonance models. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 5, pp. 791-857. http://geodesic.mathdoc.fr/item/RM_2008_63_5_a0/