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Mean‐Square Exponential Stability Analysis of Stochastic Neural Networks with Time‐Varying Delays via Fixed Point Method

Author

Listed:
  • Tianxiang Yao
  • Xianghong Lai

Abstract

This work addresses the stability study for stochastic cellular neural networks with time‐varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean‐square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.

Suggested Citation

  • Tianxiang Yao & Xianghong Lai, 2014. "Mean‐Square Exponential Stability Analysis of Stochastic Neural Networks with Time‐Varying Delays via Fixed Point Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:510358
    DOI: 10.1155/2014/510358
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    References listed on IDEAS

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    1. Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
    2. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
    3. Li, Kelin & Zhang, Xinhua & Li, Zuoan, 2009. "Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1427-1434.
    4. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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