A stochastic enterprise cluster model with mean-reverting Ornstein-Uhlenbeck process

Shuxiang Shao; Bo Du; Xiaoliang Li; Shuxiang Shao; Bo Du; Xiaoliang Li

doi:10.3934/math.2026540

AIMS Mathematics

2026, Volume 11, Issue 5: 13110-13125. doi: 10.3934/math.2026540

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A stochastic enterprise cluster model with mean-reverting Ornstein-Uhlenbeck process

Shuxiang Shao ¹,
Bo Du ^{2
,
,},
Xiaoliang Li ^{3
,
,}

1.
School of Mathematics and Sciences, Suqian University, Suqian Jiangsu, 223800, China
2.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian Jiangsu, 223300, China
3.
Jiyang College, Zhejiang Agriculture and Forestry University, Zhuji 311800, China

Received: 11 January 2026 Revised: 23 April 2026 Accepted: 27 April 2026 Published: 11 May 2026
MSC : 34B13, 60H10

In this paper, we construct and analyze a stochastic enterprise cluster model with a mean-reverting Ornstein-Uhlenbeck process. We first investigate the existence of a global unique positive solution for the system. After that, the stochastically ultimate boundedness of the system is considered. Based on a series of Lyapunov functions, sufficient criteria for the system's dynamic behaviors, including exponential extinction and persistence in the mean of the system, are established. Two numerical examples validate the theoretical results of this paper. This article provides a theoretical basis for promoting the development of enterprise clusters.
- enterprise cluster model,
- Ornstein-Uhlenbeck process,
- stochastic,
- Lyapunov function,
- extinction and persistence
Citation: Shuxiang Shao, Bo Du, Xiaoliang Li. A stochastic enterprise cluster model with mean-reverting Ornstein-Uhlenbeck process[J]. AIMS Mathematics, 2026, 11(5): 13110-13125. doi: 10.3934/math.2026540

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Abstract

In this paper, we construct and analyze a stochastic enterprise cluster model with a mean-reverting Ornstein-Uhlenbeck process. We first investigate the existence of a global unique positive solution for the system. After that, the stochastically ultimate boundedness of the system is considered. Based on a series of Lyapunov functions, sufficient criteria for the system's dynamic behaviors, including exponential extinction and persistence in the mean of the system, are established. Two numerical examples validate the theoretical results of this paper. This article provides a theoretical basis for promoting the development of enterprise clusters.

References

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