Stabilization of oscillations from a monoparametric family of the autonomous system

The problem of oscillation stabilization is solved for the autonomous system in the case when the oscillations form a monoparametric family. For each possible point type of the family the explicit formulae that solve the problem are obtained. It follows from those formulae that the dissipation is a necessary condition of the stabilization. The obtained sufficient conditions of the stabilizations coinside with the appropriate necessary conditions to within the sign of unstrict inequality.