Abstract

The paper presents a way of constructing quasimonotone nonautonomous systems ensuring x-stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U-stability on the set of non wandering points is proved to imply u-stability of quasimonotone nonlinear system and exponential u-stability on minimal attraction center provides u-stability of the total systems Examples are available.