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

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  • Xu, Liguang
  • Xu, Daoyi

Abstract

In this paper, we study impulsive stochastic 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 neural networks with mixed delays. The results extend and improve the earlier publications. An example is also discussed to illustrate the efficiency of the obtained results.

Suggested Citation

  • Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:263-272
    DOI: 10.1016/j.chaos.2007.11.031
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    1. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong & Prasad, Ashutosh, 2005. "Global robust exponential stability analysis for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 751-757.
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    4. Yang, Haifeng & Chu, Tianguang, 2007. "LMI conditions for stability of neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 557-563.
    5. 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.
    6. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    7. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    8. Mohamad, Sannay, 2007. "Exponential stability in Hopfield-type neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 456-467.
    9. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
    10. Yang, Haifeng & Chu, Tianguang & Zhang, Cishen, 2006. "Exponential stability of neural networks with variable delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 133-139.
    11. 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.
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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. 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. Wang, Xin & Zhuang, Guangming & Chen, Guoliang & Ma, Qian & Lu, Junwei, 2022. "Asynchronous mixed H∞ and passive control for fuzzy singular delayed Markovian jump system via hidden Markovian model mechanism," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    4. Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    5. 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.
    6. 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.
    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.
    8. 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).
    9. 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.

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