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Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

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  • Wang, Xiaohu
  • Xu, Daoyi

Abstract

In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.

Suggested Citation

  • Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2713-2721
    DOI: 10.1016/j.chaos.2009.03.177
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    References listed on IDEAS

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    1. Xia, Yonghui & Cao, Jinde & Huang, Zhenkun, 2007. "Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1599-1607.
    2. Xiong, Wanmin & Zhou, Qiyuan & Xiao, Bing & Yu, Yuehua, 2007. "Global exponential stability of cellular neural networks with mixed delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 896-902.
    3. Liu, Bingwen & Huang, Lihong, 2007. "Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 95-103.
    4. Zhu, Wei & Xu, Daoyi & Huang, Yumei, 2008. "Global impulsive exponential synchronization of time-delayed coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 904-912.
    5. 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.
    6. Huang, Tingwen, 2007. "Exponential stability of delayed fuzzy cellular neural networks with diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 658-664.
    7. Huang, Zai-Tang & Yang, Qi-Gui & Luo, Xiao-shu, 2008. "Exponential stability of impulsive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 770-780.
    8. Liu, Bingwen & Huang, Lihong, 2007. "Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 211-217.
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    Cited by:

    1. 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.
    2. Xinsong Yang & Chuangxia Huang & Zhichun Yang, 2012. "Stochastic Synchronization of Reaction‐Diffusion Neural Networks under General Impulsive Controller with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Xianghong Lai & Yutian Zhang, 2012. "Fixed Point and Asymptotic Analysis of Cellular Neural Networks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. 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.
    5. Xianghong Lai & Tianxiang Yao, 2013. "Exponential Stability of Impulsive Delayed Reaction‐Diffusion Cellular Neural Networks via Poincaré Integral Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Qi Luo & Xinjie Miao & Qian Wei & Zhengxin Zhou, 2013. "Stability of Impulsive Neural Networks with Time‐Varying and Distributed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Tianxiang Yao & Xianghong Lai, 2014. "Mean‐Square Exponential Stability Analysis of Stochastic Neural Networks with Time‐Varying Delays via Fixed Point Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. Yutian Zhang & Yuanhong Guan, 2013. "Asymptotic Stability of Impulsive Cellular Neural Networks with Infinite Delays via Fixed Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Jinhua Huang & Jiqing Liu & Guopeng Zhou, 2013. "Stability of Impulsive Cohen‐Grossberg Neural Networks with Time‐Varying Delays and Reaction‐Diffusion Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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