Structure of invariant sets and convergence of dynamical quasi-periodic systems

We consider systems of differential equations whose right-hand sides are quasi-periodic functions with respect to an independent variable. General properties of solutions and the structure of invariant sets of the systems are examined. Necessary and sufficient conditions for the existence of globally asymptotically stable periodic and quasi-periodic solutions are obtained.

I. Introduction

The description of real dynamical processes is carried out often by means of nonautonomous systems of differential equations or reduced to such systems.