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Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching

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  • Kao, Yonggui
  • Zhu, Quanxin
  • Qi, Wenhai

Abstract

In this paper, based on the Lyapunov second method and Razumikin techniques, we establish some novel criteria on pth moment exponential stability, almost exponential stability and instability of impulsive stochastic functional differential equations (ISFDEs) with Markovian switching. The findings show that impulsive stochastic functional equations with Markovian switching can be exponentially stabilized by impulses. Finally, an example is presented to illustrate the effectiveness and efficiency of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:795-804
    DOI: 10.1016/j.amc.2015.09.063
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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. 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.
    3. 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.
    4. 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.
    5. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
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    Cited by:

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    3. Suriguga, Ma & Kao, Yonggui & Hyder, Abd-Allah, 2020. "Uniform stability of delayed impulsive reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 372(C).
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    7. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.

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