Set-Valued Analysis

, Volume 16, Issue 5, pp 651–671

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

Article

DOI: 10.1007/s11228-007-0054-8

Cite this article as:
Li, D., Wang, Y. & Wang, S. Set-Valued Anal (2008) 16: 651. doi:10.1007/s11228-007-0054-8
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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 ℝm. 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 ℝm to obtain some interesting results. In particular, the effects of small time delays to asymptotic stability is addressed.

Keywords

Nonautonomous general dynamical systemDifferential inclusionPullback attractorStabilityRobustnessSmall time delay

Mathematics Subject Classifications (2000)

Primary 47H1758F0334C20

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