Attractivity of nonlinear impulsive delay differential
equations

Yang, Zhichun; Xu, Daoyi

doi:https://doi.org/10.1155/JAMSA/2006/83152

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 083152 | https://doi.org/10.1155/JAMSA/2006/83152

Attractivity of nonlinear impulsive delay differential equations

Zhichun Yang^1,2and Daoyi Xu¹

Received12 Oct 2005

Revised16 Jan 2006

Accepted17 Jan 2006

Published13 Jul 2006

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.

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Copyright

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.

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