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The Global Exponential Stability of the Delayed Complex-Valued Neural Networks with Almost Periodic Coefficients and Discontinuous Activations

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Abstract

In this paper, the almost periodic dynamical behaviors are considered for delayed complex-valued neural networks with discontinuous activation functions. We decomposed complex-valued to real and imaginary parts, and set an equivalent discontinuous right-hand equation. Depended on the differential inclusions theory, diagonal dominant principle, non-smooth analysis theory and generalized Lyapunov function, sufficient criteria are obtained for the existence uniqueness and global stability of almost periodic solution of the equivalent delayed differential system. Especially, we derive a series of results on the equivalent neural networks with discontinuous activations and periodic coefficients or constant coefficients, respectively. Finally, we give one numerical example to demonstrate the effectiveness of the derived theoretical results.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61403179, 61304023, 61703193 and 61773193, in part by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2017MF022, ZR2014CP008 and ZR2016JL021, and in part by the AMEP of Linyi University.

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Authors and Affiliations

  1. School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, People’s Republic of China

    Mingming Yan, Jianlong Qiu, Xiangyong Chen & Ancai Zhang

  2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Mingming Yan

  3. Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong (Linyi University), Linyi, 276005, People’s Republic of China

    Mingming Yan, Jianlong Qiu, Xiangyong Chen, Xiao Chen, Chengdong Yang & Ancai Zhang

  4. Department of Information Technology, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jianlong Qiu & Fawaz Alsaadi

  5. School of Information Science and Technology, Linyi University, Linyi, 276005, People’s Republic of China

    Xiao Chen & Chengdong Yang

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  1. Mingming Yan
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  2. Jianlong Qiu
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  3. Xiangyong Chen
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  4. Xiao Chen
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  5. Chengdong Yang
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  7. Fawaz Alsaadi
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Correspondence to Jianlong Qiu.

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Yan, M., Qiu, J., Chen, X. et al. The Global Exponential Stability of the Delayed Complex-Valued Neural Networks with Almost Periodic Coefficients and Discontinuous Activations. Neural Process Lett 48, 577–601 (2018). https://doi.org/10.1007/s11063-017-9736-x

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