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Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations

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  • Rong Gao

    (School of Economics and Management, Hebei University of Technology, Tianjin 300401, China)

Abstract

Multi-dimensional uncertain differential equation is a tool to model an uncertain multi-dimensional dynamic system. Furthermore, stability has a significant role in the field of differential equations because it can be describe the effect of the initial value on the solution of the differential equation. Hence, the concept of almost sure stability is presented concerning multi-dimensional uncertain differential equation in this paper. Moreover, a stability theorem, that is a condition, is derived to judge whether a multi-dimensional uncertain differential equation is almost surely stable or not. Additionally, the paper takes a counterexample to show that the given condition is not necessary for a multi-dimensional uncertain differential equation being almost surely stable.

Suggested Citation

  • Rong Gao, 2022. "Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3522-:d:926628
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    References listed on IDEAS

    as
    1. Sheng, Yuhong & Shi, Gang, 2019. "Stability in mean of multi-dimensional uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 178-188.
    2. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    3. Yufu Ning & Taoyong Su, 2017. "A multilevel approach for modelling vehicle routing problem with uncertain travelling time," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 683-688, March.
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