Considering the impact of the mean-reverting Ornstein–Uhlenbeck (O–U) process in an ecosystem, the stable distribution of a stochastic reaction–diffusion vegetation–water system was studied. We proved the existence and uniqueness of the global positive solution of the system by constructing the Lyapunov function. We established the existence and uniqueness of the stable distribution of the solution of the system.

中文翻译：

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具有反应-扩散的随机植被-水系统的平稳分布

考虑到均值回归 Ornstein-Uhlenbeck (O-U) 过程在生态系统中的影响，研究了随机反应-扩散植被-水系统的稳定分布。我们通过构造Lyapunov函数证明了系统全局正解的存在唯一性。我们建立了系统解的稳定分布的存在唯一性。