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Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

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  • Kuo-Shou Chiu

Abstract

We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach’s fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

Suggested Citation

  • Kuo-Shou Chiu, 2013. "Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:196139
    DOI: 10.1155/2013/196139
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    References listed on IDEAS

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    1. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    2. S. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
    3. Yuanfu Shao & Changjin Xu & Qianhong Zhang, 2012. "Globally Exponential Stability of Periodic Solutions to Impulsive Neural Networks with Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, May.
    4. Yuanfu Shao & Changjin Xu & Qianhong Zhang, 2012. "Globally Exponential Stability of Periodic Solutions to Impulsive Neural Networks with Time‐Varying Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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