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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 6723491, 8 pages
Research Article

Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Correspondence should be addressed to X. Liu; moc.361@3963126gnixuil

Received 17 April 2017; Revised 12 September 2017; Accepted 3 October 2017; Published 13 November 2017

Academic Editor: Mustafa R. S. Kulenovic

Copyright © 2017 X. Liu and Y. M. Zeng. 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.


A stability theory of nonlinear impulsive delay differential equations (IDDEs) is established. Existing algorithm may not converge when the impulses are variable. A convergent numerical scheme is established for nonlinear delay differential equations with variable impulses. Some stability conditions of analytical and numerical solutions to IDDEs are given by the properties of delay differential equations without impulsive perturbations.