Uniform attractors of periodic and asymptotically periodic dynamical systems
type: Item
instance of: scholarly article
title: Uniform attractors of periodic and asymptotically periodic dynamical systems
zbMATH Open document ID: 1082.37071
author: Peter E. Kloeden
author: Chengkui Zhong
author: Desheng Li
published in: Discrete and Continuous Dynamical Systems
publication date: 2005-04-11T00:00:00Z
review text: The authors investigate the uniform forward global attractors of periodic systems and the comparison of the dynamics between asymptotically periodic nonautonomous dynamical systems and their corresponding limiting periodic processes. First, they construct the uniform forward global attractor \(\mathcal A\) for dissipative periodic processes. Based on this result, they show the uniform Lyapunov stability of \(\mathcal A\), establish a Lyapunov functional characterization of this stability and prove the existence of an infinitesimal positively invariant neighborhood of \(\mathcal A\). Finally, they consider various types of uniform dynamics for asymptotically periodic systems and their corresponding limiting processes. The results are illustrated with examples of ordinary and delay differential equations.
reviewed by: Norbert Koksch
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 37C27
zbMATH DE Number: 2154990
zbMATH Keywords: uniform forward global attractor
zbMATH Keywords: uniform global attractor
zbMATH Keywords: semiuniform global attractor
zbMATH Keywords: periodic process
zbMATH Keywords: asymptotically periodic process
zbMATH Keywords: limiting process
MaRDI profile type: Publication
full work available at URL: dcds.2005.12.213
OpenAlex ID: W2063367580
DOI: 10.3934/DCDS.2005.12.213
description: scientific article; zbMATH DE number 2154990