Skip Navigation

IMA Journal of Mathematical Control and Information 2002 19(1 and 2):201-215; doi:10.1093/imamci/19.1_and_2.201
© 2002 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Lehman, B.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

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

Brad Lehman1

1 Department of Electrical & Computer Engineering, Northeastern University, Boston, MA 02115, USA

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.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.