Asymptotic analysis of autoresonance in the system with small dissipation

The purpose of the lecture is to show approaches for analyzing the autoresonance phenomenon occurred in oscillating systems. For the system of the model equations the existence of a Lyapunov stable solution with an unlimited growing amplitude is established. This solution describes the initial stage of the autoresonance phenomenon occurred in the system of Bloch's equations. By that a great variation of the nuclear magnetization in magnetic crystal by pumping a weak external field with the slow varying radiofrequency is proved.