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Multistability of Memristive Neural Networks with Non-monotonic Piecewise Linear Activation Functions

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Advances in Neural Networks – ISNN 2015 (ISNN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

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Abstract

In this paper, a general class of non-monotonic piecewise linear activation functions is introduced and then the coexistence and dynamical behaviors of multiple equilibrium points are studied for a class of memristive neural networks (MNNs). It is proven that under some conditions, such n-neuron MNNs can have 5n equilibrium points located in \(\Re^n\), and 3n of them are locally exponentially stable, by means of fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis. The investigation shows that the neural networks with non-monotonic piecewise linear activation functions introduced in this paper can have greater storage capacity than the ones with Mexican-hat-type activation function.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Xiaobing Nie & Jinde Cao

Authors
  1. Xiaobing Nie
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  2. Jinde Cao
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Correspondence to Xiaobing Nie .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, China

    Xiaolin Hu

  2. Fuzhou University, Fuzhou, China

    Yousheng Xia

  3. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China

    Yunong Zhang

  4. Chinese Academy of Sciences, Institute of Automation, Beijing, China

    Dongbin Zhao

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Nie, X., Cao, J. (2015). Multistability of Memristive Neural Networks with Non-monotonic Piecewise Linear Activation Functions. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-25393-0_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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