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Stability in distribution for uncertain delay differential equation

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  • Jia, Lifen
  • Sheng, Yuhong

Abstract

As a type of differential equation, uncertain delay differential equation is driven by Liu process. Stability in measure, stability in mean and stability in moment for uncertain delay differential equation have been proposed. This paper mainly gives a concept of stability in distribution, and proves a sufficient condition for uncertain delay differential equation being stable in distribution as a supplement. Moreover, this paper further discusses their relationships among stability in distribution, stability in measure, stability in mean and stability in moment.

Suggested Citation

  • Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:49-56
    DOI: 10.1016/j.amc.2018.09.037
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    References listed on IDEAS

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    1. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    2. Gao, Rong, 2017. "Uncertain wave equation with infinite half-boundary," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 28-40.
    3. Jia, Lifen & Lio, Waichon & Yang, Xiangfeng, 2018. "Numerical method for solving uncertain spring vibration equation," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 428-441.
    4. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
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    Cited by:

    1. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "The almost sure stability for uncertain delay differential equations based on normal lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Wang, Xiao & Ning, Yufu & Peng, Zhen, 2020. "Some results about uncertain differential equations with time-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    4. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    5. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "Parameter estimation in uncertain delay differential equations via the method of moments," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    6. Gao, Yin & Jia, Lifen, 2021. "Stability in mean for uncertain delay differential equations based on new Lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    7. Lu, Ziqiang & Zhu, Yuanguo, 2023. "Asymptotic stability in pth moment of uncertain dynamical systems with time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 323-335.
    8. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    9. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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