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

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.