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Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

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  • Ruofeng Rao
  • Shouming Zhong

Abstract

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Ruofeng Rao & Shouming Zhong, 2017. "Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory," Complexity, Hindawi, vol. 2017, pages 1-9, September.
    • Handle: RePEc:hin:complx:6292597
    DOI: 10.1155/2017/6292597
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhilin Pu, 2013. "LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    2. Kwiecinska, Anna A., 1999. "Stabilization of partial differential equations by noise," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 179-184, February.
    3. Li, Xiaodi & Deng, Feiqi, 2017. "Razumikhin method for impulsive functional differential equations of neutral type," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 41-49.
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