A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

中文翻译：

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具有 Ornstein-Uhlenbeck 过程的广义随机竞争系统

本文提出了一个具有随机扰动的广义竞争系统，其中随机扰动由著名的 Ornstein-Uhlenbeck 过程描述。通过比较定理、Itô积分公式、Chebyshev不等式、鞅性质等随机微分方程的理论，得到系统全局正解的存在性和唯一性。然后分别导出了物种几乎肯定灭绝的充分条件、均值持久性和系统的随机持久性。最后通过一系列数值算例直观地验证了理论分析结果的可行性和正确性。而且，