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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 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.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Desheng Li

  2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Yejuan Wang

  3. Department of Mathematics, Lanzhou City University, Lanzhou, 730070, People’s Republic of China

    Suyun Wang

Authors
  1. Desheng Li
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  2. Yejuan Wang
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  3. Suyun Wang
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Correspondence to Yejuan Wang.

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Li, D., Wang, Y. & Wang, S. On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions. Set-Valued Anal 16, 651–671 (2008). https://doi.org/10.1007/s11228-007-0054-8

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  • DOI: https://doi.org/10.1007/s11228-007-0054-8

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