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Multistability analysis of competitive neural networks with Gaussian-wavelet-type activation functions and unbounded time-varying delays

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  • Nie, Xiaobing
  • Liang, Jinling
  • Cao, Jinde

Abstract

This paper investigates the coexistence and local stability of multiple equilibrium points for competitive neural networks, where the Gaussian-wavelet-type activation functions are employed and the unbounded time-varying delays are considered. Based on geometric formulation, the fixed point theorem, contraction mapping theorem and rigorous mathematical analysis, a series of sufficient conditions are derived to ascertain that the addressed neural networks have exactly 5n equilibrium points, among which 3n equilibrium points are locally stable. On this basis, some criteria are also obtained on the multiple exponential stability, multiple power stability and multiple log-stability of Hopfield neural networks with Gaussian-wavelet-type activation functions. The obtained results generalize and improve the existing multistability results of Hopfield neural networks and competitive neural networks without time delays and with Gaussian-wavelet-type activation functions. Moreover, it is highlighted that the competitive neural networks with Gaussian-wavelet-type activation functions can have both more total equilibrium points and more locally stable equilibrium points than the ones with Mexican-hat-type activation function. Finally, two numerical examples with computer simulations are provided to illustrate and validate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:449-468
    DOI: 10.1016/j.amc.2019.03.026
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    References listed on IDEAS

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    1. Xiaobing Nie & Jinde Cao & Shumin Fei, 2014. "Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-20, May.
    2. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
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    Cited by:

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    2. Yao, Wei & Wang, Chunhua & Sun, Yichuang & Zhou, Chao & Lin, Hairong, 2020. "Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    5. 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.

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