Asymptotic analysis of autoresonance models

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.