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Global exponential stability of uncertain memristor-based recurrent neural networks with mixed time delays

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Abstract

The global exponential stability of the equilibrium point for uncertain memristor-based recurrent neural networks is studied in this paper. The memristor-based recurrent neural networks considered in this paper are based on a realistic memristor model, and can be considered as the extension of some existing memristor-based recurrent neural networks. By virtue of homomorphic theory, it is proved that the uncertain memristor-based recurrent neural networks have a unique equilibrium point under some mild assumptions. Moreover, the unique equilibrium point is proved to be globally exponentially stable by constructing a suitable Lyapunov functional. Finally, the obtained results are applied to determine the dynamical behaviors and circuit design of the memristor-based recurrent neural networks by some numerical examples.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant (11201100, 11401142, 61403101), and Heilongjiang Province Science and Technology Agency Funds of China (A201213).

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Authors and Affiliations

  1. Department of Electronic Science and Technology, Harbin University of Science and Technology, Harbin, 150080, People’s Republic of China

    Jianmin Wang

  2. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, People’s Republic of China

    Fengqiu Liu

  3. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, People’s Republic of China

    Sitian Qin

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  1. Jianmin Wang
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  2. Fengqiu Liu
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  3. Sitian Qin
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Correspondence to Jianmin Wang.

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Wang, J., Liu, F. & Qin, S. Global exponential stability of uncertain memristor-based recurrent neural networks with mixed time delays. Int. J. Mach. Learn. & Cyber. 10, 743–755 (2019). https://doi.org/10.1007/s13042-017-0759-4

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  • DOI: https://doi.org/10.1007/s13042-017-0759-4

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