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Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

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  • Wang, Xiaohu
  • Guo, Qingyi
  • Xu, Daoyi

Abstract

In this paper, we study the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. By establishing an L-operator differential inequality with mixed delays and using the properties of M-cone and stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. These results generalize a few previous known results and remove some restrictions on the neural networks. Two examples are also discussed to illustrate the efficiency of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:5:p:1698-1710
    DOI: 10.1016/j.matcom.2008.08.008
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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. Chen, Zhang & Ruan, Jiong, 2007. "Global dynamic analysis of general Cohen–Grossberg neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1830-1837.
    3. Zhao, Hongyong & Ding, Nan, 2007. "Dynamic analysis of stochastic bidirectional associative memory neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1692-1702.
    4. Zhao, Weirui & Tan, Yong, 2007. "Harmless delays for global exponential stability of Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 47-57.
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    Cited by:

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    2. Cao, Wenping & Zhu, Quanxin, 2021. "Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    3. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    4. Li, Liangliang & Jian, Jigui, 2015. "Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 860-873.
    5. 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.
    6. Peng, Shiguo & Jia, Baoguo, 2010. "Some criteria on pth moment stability of impulsive stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1085-1092, July.
    7. Li, Dingshi & He, Danhua & Xu, Daoyi, 2012. "Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1531-1543.

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