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Stability of hybrid stochastic functional differential equations

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  • Ruan, Dehao
  • Xu, Liping
  • Luo, Jiaowan

Abstract

In this paper, a class of hybrid stochastic functional differential equations is investigated. Under some suitable assumptions, the pth moment stability, asymptotic stability and exponential stability are discussed by means of constructing an auxiliary functional differential equation and using the comparison principle. The proposed criteria removes some conditions in some earlier publications. Moreover, two examples and simulations are given to illustrate our results.

Suggested Citation

  • Ruan, Dehao & Xu, Liping & Luo, Jiaowan, 2019. "Stability of hybrid stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 832-841.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:832-841
    DOI: 10.1016/j.amc.2018.03.064
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    References listed on IDEAS

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    1. Xie, Jing & Kao, Yonggui & Wang, Changhong & Gao, Cunchen, 2015. "Delay-dependent robust stability of uncertain neutral-type Itoˆ stochastic systems with Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 576-585.
    2. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    3. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    4. You, Surong & Mao, Wei & Mao, Xuerong & Hu, Liangjian, 2015. "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 73-83.
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    Cited by:

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    2. Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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