Uniform attractors of periodic and asymptotically periodic dynamical systems

P.E. Kloeden; Desheng Li; Chengkui Zhong

doi:10.3934/dcds.2005.12.213

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2005, Volume 12, Issue 2: 213-232. Doi: 10.3934/dcds.2005.12.213

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Uniform attractors of periodic and asymptotically periodic dynamical systems

1.
FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
2.
Department of Mathematics and Information Science, Yantai University, Yantai 264005
3.
Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000

Received: July 31, 2003

Revised: June 30, 2004

Published: January 2005

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Abstract

The uniform forward global attractors of periodic systems and the comparison of the dynamics between asymptotically periodic non-autonomous dynamical systems and their corresponding limiting periodic processes are investigated. The existence and Lyapunov stability of such attractors are established and a Lyapunov functional charecterization of uniform forward global attractors of non-autonomous periodic processes is presented. The results are illustrated with examples of ordinary and delay differential equations.

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Mathematics Subject Classification: 47H17, 58F03, 34C20, 34D20.

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