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Global exponential stability of impulsive stochastic functional differential systems

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  • Cheng, Pei
  • Deng, Feiqi

Abstract

In this paper, based on the Razumikhin techniques and Lyapunov functions, several criteria on the global exponential stability and instability of impulsive stochastic functional differential systems are obtained. Our results show that stochastic functional differential systems may be exponentially stabilized by impulses. Two illustrative examples are given to show the effectiveness of the results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1854-1862
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    References listed on IDEAS

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    1. 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.
    2. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    3. 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.
    4. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    5. Mao, Xuerong, 1996. "Razumikhin-type theorems on exponential stability of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 233-250, December.
    6. 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.
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    Cited by:

    1. Lijun Pan & Jinde Cao & Yong Ren, 2020. "Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
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    4. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    5. Yao, Fengqi & Deng, Feiqi, 2012. "Exponential stability in terms of two measures of impulsive stochastic functional differential systems via comparison principle," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1151-1159.

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