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Abstract and Applied Analysis
Volume 2014, Article ID 327070, 14 pages
Research Article

Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

1School of Mathematics, Shandong University, Jinan 250100, China
2School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China

Received 22 January 2014; Revised 16 March 2014; Accepted 25 March 2014; Published 15 May 2014

Academic Editor: Ivanka Stamova

Copyright © 2014 Qiang Xi and Jianguo Si. 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.


We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results.