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Multistability analysis of state-dependent switched Hopfield neural networks with the Gaussian-wavelet-type activation function

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  • Liu, Yang
  • Wang, Zhen
  • Huang, Xia

Abstract

In multistability analysis, the Gaussian-wavelet-type activation function is shown to have better properties by comparison with sigmoidal functions, saturated functions and Mexican-hat-type functions. State-dependent switched Hopfield neural network (SSHNN) is expected to display even richer dynamical behaviors in contrast with conventional Hopfield neural networks (HNNs). Considering these two reasons, this paper studies the multistability of SSHNNs with the Gaussian-wavelet-type activation function. Some sufficient conditions for the coexistence as well as the stability of multiple equilibria of SSHNNs are derived. It is obtained that SSHNNs with the Gaussian-wavelet-type activation function can have at least 7n or 6n equilibria, of which 4n or 5n are locally stable (LS). We find that, compared with conventional HNNs with the Gaussian-wavelet-type activation function or SSHNNs with other kinds of activation functions, SSHNNs with the Gaussian-wavelet-type activation functions can have more LS equilibria. It implies that SSHNNs with the Gaussian-wavelet-type activation functions have even larger storage capacity and have overwhelming superiority in associative memory applications. Lastly, some simulation results are given to verify the correctness of the theoretical results.

Suggested Citation

  • Liu, Yang & Wang, Zhen & Huang, Xia, 2022. "Multistability analysis of state-dependent switched Hopfield neural networks with the Gaussian-wavelet-type activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 232-250.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:232-250
    DOI: 10.1016/j.matcom.2022.01.021
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    References listed on IDEAS

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    1. Nie, Xiaobing & Liang, Jinling & Cao, Jinde, 2019. "Multistability analysis of competitive neural networks with Gaussian-wavelet-type activation functions and unbounded time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 449-468.
    2. Liu, Yunfeng & Song, Zhiqiang & Tan, Manchun, 2019. "Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 1-17.
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