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Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms

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  • Zhao, Hongyong
  • Mao, Zisen

Abstract

In this paper, we study a class of nonautonomous cellular neural networks with reaction-diffusion terms. By employing the method of variation parameter, applying inequality technique and introducing a lot of real parameters, we present some sufficient conditions ensuring the boundedness and globally exponential stability of the solutions for nonautonomous cellular neural networks with reaction-diffusion terms. The results obtained extend and improve the earlier publications. Finally, three examples with their numerical simulations are provided to show the correctness of our analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:5:p:1603-1617
    DOI: 10.1016/j.matcom.2008.07.008
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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. 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.
    3. Sun, Changyin & Feng, Chun-Bo, 2004. "Exponential periodicity and stability of delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 469-478.
    4. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Xinggui Li & Xinsong Yang, 2023. "Global Stabilization of Delayed Feedback Financial System Involved in Advertisement under Impulsive Disturbance," Mathematics, MDPI, vol. 11(9), pages 1-12, April.

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