Journal Article

The influence of delays when averaging slow and fast oscillating systems: overview

Brad Lehman

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 19, issue 1_and_2, pages 201-215
Published in print March 2002 | ISSN: 0265-0754
Published online March 2002 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/19.1_and_2.201
The influence of delays when averaging slow and fast oscillating systems: overview

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This paper presents an overview of results in averaging theory. First, averaging for ordinary differential equations (ODEs) is presented. These results are then applied to fast oscillating differential equations to show how zero average perturbations can affect stability properties. Next, averaging for functional differential equations (FDEs) is presented. A comparison of ‘classical’ averaged models and more recently developed averaged models for FDEs is given. Then the FDE averaging results are applied to fast oscillating delay differential equations. It is explained that fast oscillating FDEs are often sensitive to extremely small delays. Several examples are presented in this paper to help give an overview of results.

Keywords: averaging; delay; stability

Journal Article.  0 words. 

Subjects: Mathematics

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