On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

This paper is concerned with the dynamics of nonautonomous general dynamical systems (NAGDSs in short) and applications to differential inclusions on ? ^m . First, we show that if a NAGDS has a compact uniformly attracting set, then it has a pullback attractor $\mathcal{A}$ with the parametrically inflated pullback attractor $\mathcal{A}(\varepsilon_0)$ being uniformly forward attracting. Then, we establish some stability results for pullback attractors. Finally, we apply the abstract theory to nonautonomous differential inclusions on ? ^m to obtain some interesting results. In particular, the effects of small time delays to asymptotic stability is addressed.