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μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory

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Abstract

In this paper, the μ-stability of multiple equilibrium points (EPs) in the Cohen-Grossberg neural networks (CGNNs) is addressed by designing a kind of discontinuous activation function (AF). Under some criteria, CGNNs with this AF are shown to possess at least 5n EPs, of which 3n EPs are locally μ-stable. Compared with the saturated AF or the sigmoidal AF, CGNNs with the designed AF can produce many more total/stable EPs. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they can store more prototype patterns. Moreover, the AF is expanded to a more general version to further increase the number of total/stable equilibria. The CGNNs with the expanded AF are found to produce (2k + 3)n EPs, of which (k + 2)n EPs are locally μ-stable. By adjusting two parameters in the AF, the number of sufficient conditions ensuring the stability of multiple equilibria can be decreased. This finding implies that the computational complexity can be greatly reduced. Two numerical examples and an application to associative memory are illustrated to verify the correctness of the obtained results.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yang Liu & Zhen Wang

  2. College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Min Xiao

  3. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    YuXia Li

  4. Electrical and Information Engineering, Anhui University of Technology, Ma’anshan, 243002, China

    Hao Shen

Authors
  1. Yang Liu
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  2. Zhen Wang
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  3. Min Xiao
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  4. YuXia Li
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  5. Hao Shen
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Corresponding author

Correspondence to Zhen Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62173214 and 61973199), the Shandong Provincial Natural Science Foundation (Grant Nos. ZR2021MF003 and ZR2022MF324), and the Major Technologies Research and Development Special Program of Anhui Province (Grant No. 202003a05020001).

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Liu, Y., Wang, Z., Xiao, M. et al. μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory. Sci. China Technol. Sci. 66, 2611–2624 (2023). https://doi.org/10.1007/s11431-022-2311-1

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  • DOI: https://doi.org/10.1007/s11431-022-2311-1

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