Abstract and Applied Analysis
Volume 2012 (2012), Article ID 210156, 10 pages
http://dx.doi.org/10.1155/2012/210156
Research Article

Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

T. S. Doan1,2 and S. Siegmund3

1Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi 10307, Vietnam
3Center for Dynamics, TU Dresden, 01062 Dresden, Germany

Received 23 April 2012; Accepted 6 June 2012

Academic Editor: Agacik Zafer

Copyright © 2012 T. S. Doan and S. Siegmund. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.