On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions |
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Authors: | Desheng Li Peter E Kloeden |
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Institution: | a Department of Mathematics, Tianjin University, Tianjin 300072, PR China b FB Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany |
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Abstract: | We establish the existence and stability results for periodic nonautonomous uniform forward attractors of periodic general dynamical systems (set-valued dynamical systems). We also investigate the dynamical behavior of nonautonomous periodic differential inclusion x′(t)∈f(t,x(t)) on Rm with only upper semi-continuous right-hand side by applying the abstract results. Firstly, we show that if the system has a compact uniformly attracting set, then it has a periodic nonautonomous uniform forward attractor A. Secondly, we prove that A is robust with respect to both internal and external perturbations. Finally, we apply the robustness result to discuss the effects of small time delays to asymptotic stability of the system. |
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Keywords: | Periodic General dynamical system Differential inclusion Uniform forward attractor Existence Stability Robustness Small time delay |
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