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Mean Square Asymptotic Stability of Discrete-Time Fractional Order Stochastic Neural Networks with Multiple Time-Varying Delays

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Abstract

In this paper, the mean square locally and globally asymptotic stability problem of discrete-time fractional order stochastic neural networks(DFOSNNs) with multiple time-varying delays are investigated. Firstly, the DFOSNNs model with multiple time-varying delays are established. Then, the general framework for the mixed delays Halanay-type inequality has been established with no harsh assumption. Further, the locally and globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense are proved via Halanay-type inequality respectively. In addition, the sufficient condition for globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense is derived via Lyapunov–Krasovskii functional method. From the results obtained in this paper, the two theorems of global asymptotic stability are complement each other. Finally, three numerical examples are given to show the validity of the obtained theoretical results.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 62003026, 62173027) and the Fundamental Research Funds for the Central Universities (Grant No. 2020RC103).

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Authors and Affiliations

  1. School of mathematics and statistics, Beijing Jiaotong University, Beijing, 100044, China

    Dongsheng Yang, Yongguang Yu, Wei Hu, Xiaolin Yuan & Guojian Ren

  2. Insitute of Systems Science, Beijing Jiaotong University, Beijing, 100044, China

    Wei Hu

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  1. Dongsheng Yang
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  2. Yongguang Yu
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  3. Wei Hu
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  4. Xiaolin Yuan
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Correspondence to Guojian Ren.

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Yang, D., Yu, Y., Hu, W. et al. Mean Square Asymptotic Stability of Discrete-Time Fractional Order Stochastic Neural Networks with Multiple Time-Varying Delays. Neural Process Lett 55, 9247–9268 (2023). https://doi.org/10.1007/s11063-023-11200-9

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