Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 83152, 12 pages
doi:10.1155/JAMSA/2006/83152

Attractivity of nonlinear impulsive delay differential equations

Zhichun Yang1,2 and Daoyi Xu1

1Mathematical College, Sichuan University, Chengdu 610064, China
2Department of Mathematics, Chongqing Normal University, Chongqing 400047, China

Received 12 October 2005; Revised 16 January 2006; Accepted 17 January 2006

Copyright © 2006 Zhichun Yang and Daoyi Xu. 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

The attractivity of nonlinear differential equations with time delays and impulsive effects is discussed. We obtain some criteria to determine the attracting set and attracting basin of the impulsive delay system by developing an impulsive delay differential inequality and introducing the concept of nonlinear measure. Examples and their simulations illustrate the effectiveness of the results and different asymptotical behaviors between the impulsive system and the corresponding continuous system.