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Algebraic conditions of stability for hopfield neural network

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Abstract

Using the relationship between the resistance, capacitance and current in Hopfield neural network, and the properties of sigmoid function, this paper gives the terse, explicit algebraical criteria of global exponential stability, global asymptotical stability and instability. Then this paper makes clear the essence of the stability that Hopfield defined, and provides a theoretical foundation for the design of a network.

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Authors and Affiliations

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

    Liao Xiaoxin & Zeng Zhigang

  2. Department of Statistics and Modeling, Science University of Strathclyde, G1 IXH, Glasgow, UK

    Mao Xuerong

  3. Department of Automation and Computer-aided Engineering, the Chinese University of Hong Kong, Shatin, Hong Kong, China

    Wang Jun

Authors
  1. Liao Xiaoxin
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  2. Mao Xuerong
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  3. Wang Jun
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  4. Zeng Zhigang
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Corresponding author

Correspondence to Liao Xiaoxin.

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Liao, X., Mao, X., Wang, J. et al. Algebraic conditions of stability for hopfield neural network. Sci China Ser F 47, 113–125 (2004). https://doi.org/10.1360/02yf0206

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  • DOI: https://doi.org/10.1360/02yf0206

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