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Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays

Author

Listed:
  • Shifang Kuang
  • Yunjian Peng
  • Feiqi Deng
  • Wenhua Gao

Abstract

Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an equilibrium are given. Under the conditions which guarantee the stability of the analytical solution, the Euler‐Maruyama scheme and the split‐step backward Euler scheme are proved to be mean‐square stable. At last, an example is given to demonstrate our results.

Suggested Citation

  • Shifang Kuang & Yunjian Peng & Feiqi Deng & Wenhua Gao, 2013. "Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:761237
    DOI: 10.1155/2013/761237
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    References listed on IDEAS

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    1. Qiyong Li & Siqing Gan, 2012. "Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, February.
    2. Minghui Song & Hui Yu, 2012. "Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii‐Type Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Qiyong Li & Siqing Gan, 2012. "Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Minghui Song & Hui Yu, 2012. "Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, September.
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    Cited by:

    1. Liang Liu & Zhandong Yu & Qi Zhou & Hamid Reza Karimi, 2013. "State‐Feedback Stabilization for a Class of Stochastic Feedforward Nonlinear Time‐Delay Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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