, Volume 16, Issue 5-6, pp 651-671
Date: 19 Jul 2007

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

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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.