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Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions

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  • Liu, Yunfeng
  • Song, Zhiqiang
  • Tan, Manchun

Abstract

In this paper, the multistability and multiperiodicity problems are investigated for the memristor-based fuzzy cellular neural networks (MFCNNs) with nonmonotonic activation functions and unbounded time-varying delays. Based on the fixed point theorem and the geometrical properties of activation functions, sufficient criteria are obtained to ensure such n-neuron MFCNNs can have at least ∏i=1n(2Ki+1) equilibrium points with Ki>0 in which ∏i=1n(Ki+1) are locally μ-stable. As an extension of the theory, the existence of ∏i=1n(Ki+1) locally exponentially stable periodic solutions with time-periodic inputs is also derived. Finally, one example is presented to confirm our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:159:y:2019:i:c:p:1-17
    DOI: 10.1016/j.matcom.2018.10.007
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    References listed on IDEAS

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    1. Huang, Chuangxia & Huang, Lihong & Yuan, Zhaohui, 2005. "Global stability analysis of a class of delayed cellular neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 133-148.
    2. Yu, Juan & Hu, Cheng & Jiang, Haijun & Teng, Zhidong, 2012. "Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 895-908.
    3. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    4. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    5. Zhao, Hongyong & Mao, Zisen, 2009. "Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1603-1617.
    6. 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:

    1. Zhang, Hai & Cheng, Yuhong & Zhang, Weiwei & Zhang, Hongmei, 2023. "Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 846-857.
    2. 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.
    3. Zhao, Rui & Wang, Baoxian & Jian, Jigui, 2022. "Global μ-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 223-245.

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