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Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms

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  • Li, Zuoan
  • Li, Kelin

Abstract

In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:492-499
    DOI: 10.1016/j.chaos.2009.01.018
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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. Li, Kelin & Zhang, Xinhua & Li, Zuoan, 2009. "Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1427-1434.
    3. 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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    6. Li, Yongkun & Xing, Wenya & Lu, Linghong, 2006. "Existence and global exponential stability of periodic solution of a class of neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 437-445.
    7. Huang, Tingwen, 2007. "Exponential stability of delayed fuzzy cellular neural networks with diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 658-664.
    8. Wang, Jian & Lu, Jun Guo, 2008. "Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 878-885.
    9. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    10. Lu, Jun Guo & Lu, Lin Ji, 2009. "Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1538-1549.
    11. 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.
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    Cited by:

    1. Stamova, Ivanka & Stamov, Trayan & Stamov, Gani, 2022. "Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Gani Stamov & Stefania Tomasiello & Ivanka Stamova & Cvetelina Spirova, 2019. "Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms," Mathematics, MDPI, vol. 8(1), pages 1-20, December.
    3. Zhang, Yutian & Luo, Qi, 2012. "Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1033-1040.
    4. Fei Luo & Weiyi Hu & Enli Wu & Xiufang Yuan, 2024. "Global Exponential Stability of Impulsive Delayed Neural Networks with Parameter Uncertainties and Reaction–Diffusion Terms," Mathematics, MDPI, vol. 12(15), pages 1-15, July.

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