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Global stability analysis of a class of delayed cellular neural networks

Author

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  • Huang, Chuangxia
  • Huang, Lihong
  • Yuan, Zhaohui

Abstract

Employing Brouwer’s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors study further global exponential stability and the existence of periodic solutions of a class of cellular neural networks with delays (DCNNs) in this paper. A family of sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of DCNNs. The results extend and improve the earlier publications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:3:p:133-148
    DOI: 10.1016/j.matcom.2005.06.001
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    Citations

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    Cited by:

    1. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    2. Zhang, Yinping, 2009. "Stationary oscillation for cellular neural networks with time delays and impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3174-3178.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Global exponential stability for nonautonomous cellular neural networks with unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1144-1151.
    4. Zhu, Song & Shen, Yi & Chen, Guici, 2012. "Noise suppress exponential growth for hybrid Hopfield neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 10-20.
    5. Wang, Xiaohu & Guo, Qingyi & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1698-1710.
    6. 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.
    7. Singh, Vimal, 2007. "LMI approach to the global robust stability of a larger class of neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1927-1934.
    8. 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.
    9. Long, Shujun & Wang, Xiaohu & Li, Dingshi, 2012. "Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2199-2214.
    10. Huang, Zhenkun & Wang, Xinghua & Xia, Yonghui, 2009. "A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1121-1131.
    11. Zhao, Weirui & Zhang, Huanshui, 2009. "New results of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 831-838.
    12. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
    13. Zhou, Tiejun & Liu, Yuehua & Li, Xiaoping & Liu, Yirong, 2009. "A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 332-341.

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