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Boundedness and exponential stability for nonautonomous cellular neural networks with reaction–diffusion terms

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  • Lou, Xuyang
  • Cui, Baotong

Abstract

Employing Lyapunov functional method, we analyze the ultimate boundedness and global exponential stability of a class of reaction–diffusion cellular neural networks with time-varying delays. Some new criteria are obtained to ensure ultimate boundedness and global exponential stability of delayed reaction–diffusion cellular neural networks (DRCNNs). Without assuming that the activation functions fijl(·) are bounded, the results extend and improve the earlier publications.

Suggested Citation

  • Lou, Xuyang & Cui, Baotong, 2007. "Boundedness and exponential stability for nonautonomous cellular neural networks with reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 653-662.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:653-662
    DOI: 10.1016/j.chaos.2006.01.044
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    References listed on IDEAS

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    1. Cui, Bao Tong & Lou, Xu Yang, 2006. "Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1347-1354.
    2. Lu, Junwei & Guo, Yiqian & Xu, Shengyuan, 2006. "Global asymptotic stability analysis for cellular neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 349-353.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2006. "Stability analysis for cellular neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 331-336.
    4. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "Delay-dependent exponential stability of cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1363-1369.
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    Cited by:

    1. 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.
    2. Lou, Xuyang & Cui, Baotong, 2009. "Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2188-2197.
    3. Sheng, Li & Yang, Huizhong & Lou, Xuyang, 2009. "Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 930-939.
    4. Wang, Linshan & Zhang, Yan & Zhang, Zhe & Wang, Yangfan, 2009. "LMI-based approach for global exponential robust stability for reaction–diffusion uncertain neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 900-905.
    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. Li, Zuoan & Li, Kelin, 2009. "Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 492-499.
    7. Gao, Ming & Cui, Baotong, 2009. "Robust exponential stability of interval Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1914-1928.

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