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Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms

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  • Mingzhu Song
  • Quanxin Zhu
  • Hongwei Zhou

Abstract

The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks.

Suggested Citation

  • Mingzhu Song & Quanxin Zhu & Hongwei Zhou, 2016. "Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:2487957
    DOI: 10.1155/2016/2487957
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    References listed on IDEAS

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    1. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
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