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Multistability of periodic delayed recurrent neural network with memristors

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Abstract

This paper discusses the recurrent neural network (RNN) with memristors as connection weights. Memristor is a nonlinear resistor. Memristance varies periodically with time when the sinusoidal voltage source is applied. According to this property of memristor, it shows that coefficients of RNN with memristors are periodic functions with respect to time t. By dividing the state space and using contraction mapping theorem, one sufficient condition is obtained for multiperiodicity. And the periodic orbits located in saturation regions are locally exponentially stable limit cycles. At last, one example is given for verifying the validity of our result.

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Acknowledgments

The work is supported by the Natural Science Foundation of China under Grant 60974021, the Key Program of National Natural Science of China under Grant 61134012 and 61125303, the 973 Program of China under Grant 2011CB710606, the Fund for Distinguished Young Scholars of Hubei Province under Grant 2010CDA081.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Gang Bao & Zhigang Zeng

  2. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Gang Bao & Zhigang Zeng

Authors
  1. Gang Bao
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  2. Zhigang Zeng
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Correspondence to Gang Bao.

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Bao, G., Zeng, Z. Multistability of periodic delayed recurrent neural network with memristors. Neural Comput & Applic 23, 1963–1967 (2013). https://doi.org/10.1007/s00521-012-0954-x

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  • DOI: https://doi.org/10.1007/s00521-012-0954-x

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