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Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions

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Abstract

The target of this article is to study almost periodic dynamical behaviors for complex-valued recurrent neural networks with discontinuous activation functions and time-varying delays. We construct an equivalent discontinuous right-hand equation by decomposing real and imaginary parts of complex-valued neural networks. Based on differential inclusions theory, diagonal dominant principle and nonsmooth analysis theory of generalized Lyapunov function method, we achieve the existence, uniqueness and global stability of almost periodic solution for the equivalent delayed differential network. In particular, we derive a series of results on the equivalent neural networks with discontinuous activation functions, constant coefficients as well as periodic coefficients, respectively. Finally, we give a numerical example to demonstrate the effectiveness and feasibility 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. 61273012, 61403179, 61304023 and 61503171, in part by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2014AL009, ZR2014CP008 and ZR2015FL021 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, China

    Mingming Yan, Jianlong Qiu, Xiangyong Chen & Ancai Zhang

  2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China

    Mingming Yan

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jianlong Qiu

  4. School of Informatics, Linyi University, Linyi, 276005, China

    Xiao Chen & Chengdong Yang

  5. Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jianlong Qiu

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  1. Mingming Yan
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  2. Jianlong Qiu
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  4. Xiao Chen
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  5. Chengdong Yang
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Correspondence to Jianlong Qiu.

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Yan, M., Qiu, J., Chen, X. et al. Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions. Neural Comput & Applic 30, 3339–3352 (2018). https://doi.org/10.1007/s00521-017-2911-1

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  • DOI: https://doi.org/10.1007/s00521-017-2911-1

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