Abstract
This paper is concerned with the dynamics of nonautonomous general dynamical systems (NAGDSs in short) and applications to differential inclusions on ℝ 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 ℝ m to obtain some interesting results. In particular, the effects of small time delays to asymptotic stability is addressed.
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