Global attracting sets and exponential stability of nonlinear uncertain differential equations

Yurou Deng; Zhi Li; Liping Xu; Yurou Deng; Zhi Li; Liping Xu

doi:10.3934/math.20231366

AIMS Mathematics

2023, Volume 8, Issue 11: 26703-26714. doi: 10.3934/math.20231366

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Research article

Global attracting sets and exponential stability of nonlinear uncertain differential equations

School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

Received: 25 April 2023 Revised: 24 July 2023 Accepted: 23 August 2023 Published: 19 September 2023
MSC : 60G15, 60H05, 60H15

Uncertain differential equation is a type of differential equation driven by canonical Liu process. By applying some uncertain theories, the sufficient conditions of the exponential stability in mean square is obtained for nonlinear uncertain differential equations. At the same time, some new criteria ensuring the existence of the global attracting sets of considered equations are presented.
- canonical Liu process,
- uncertain differential equation,
- exponential stability,
- global attracting set
Citation: Yurou Deng, Zhi Li, Liping Xu. Global attracting sets and exponential stability of nonlinear uncertain differential equations[J]. AIMS Mathematics, 2023, 8(11): 26703-26714. doi: 10.3934/math.20231366

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Abstract

Uncertain differential equation is a type of differential equation driven by canonical Liu process. By applying some uncertain theories, the sufficient conditions of the exponential stability in mean square is obtained for nonlinear uncertain differential equations. At the same time, some new criteria ensuring the existence of the global attracting sets of considered equations are presented.

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