Stability in mean for uncertain multiple-delay differential equations

Yin Gao, Yilin Yang and Han Tang

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: Differential equations with multiple delays that are driven by the Liu process find applications in systems featuring multiple delays. These include ecological systems, virus distribution systems, and power systems, and they are referred to as uncertain multiple-delay differential equations. Currently, research has been conducted on the existence and uniqueness theorem, as well as the measure stability of the solutions for uncertain multiple-delay differential equations. To meet the requirements for different types of stability, this paper defines the stability in mean for uncertain multiple-delay differential equations. By relying on the Lipschitz conditions, several sufficient theorems regarding the stability in mean of uncertain multiple-delay differential equations are successfully proved. As an expansion of the Lipschitz conditions, two sufficient theorems of the stability in mean for uncertain multiple-delay differential equations are demonstrated using special Lipschitz conditions. In addition, several numerical examples are utilized to validate the effectiveness of the above mentioned sufficient theorems.

Keywords: Stability in mean; Uncertain multiple-delay differential equations; Liu process; Uncertainty theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012305

DOI: 10.1016/j.chaos.2025.117217

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