Set-Valued Analysis

, Volume 16, Issue 5–6, pp 651–671 | Cite as

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

Article

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.

Keywords

Nonautonomous general dynamical system Differential inclusion Pullback attractor Stability Robustness Small time delay 

Mathematics Subject Classifications (2000)

Primary 47H17 58F03 34C20 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsTianjin UniversityTianjinPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  3. 3.Department of MathematicsLanzhou City UniversityLanzhouPeople’s Republic of China

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