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Stability analysis of stochastic reaction–diffusion neural networks with Markovian switching and time delays in the leakage terms

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Abstract

This paper investigates a class of stochastic reaction–diffusion neural networks with both Markovian jumping parameters and time delays in the leakage terms. By using the Lyapunov functional method, linear matrix inequality approach and stochastic analysis technique, a novel sufficient condition is derived to ensure the stochastic stability of the networks in the mean square sense. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab LMI Toolbox. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.

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Authors and Affiliations

  1. School of Science, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Cheng-De Zheng & Yue Zhang

  2. School of Information Science and Engineering, Northeastern University, Shenyang, 110004, People’s Republic of China

    Zhanshan Wang

Authors
  1. Cheng-De Zheng
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  2. Yue Zhang
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  3. Zhanshan Wang
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Corresponding author

Correspondence to Cheng-De Zheng.

Additional information

This work was supported by the National Natural Science Foundation of China under Grants 61074073, 61034005, 61273022, Program for New Century Excellent Talents in University of China (NCET-10-0306), and the Fundamental Research Funds for the Central Universities under Grants N110504001.

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Zheng, CD., Zhang, Y. & Wang, Z. Stability analysis of stochastic reaction–diffusion neural networks with Markovian switching and time delays in the leakage terms. Int. J. Mach. Learn. & Cyber. 5, 3–12 (2014). https://doi.org/10.1007/s13042-013-0165-5

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  • DOI: https://doi.org/10.1007/s13042-013-0165-5

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