In this paper, a mutualism model with stochastic perturbations is considered and some of its coefficients are related to time. Under some assumptions, we make efforts to prove the existence and uniqueness of a positive solution, and the asymptotic behavior to the problem is discussed. Furthermore, we also prove the properties of stochastic boundedness, uniform continuity and stochastic permanence of this system. At last, some numerical simulations are introduced to illustrate our main results.

中文翻译：

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随机环境中具有时间相关系数的共生模型分析

在本文中，考虑了一个具有随机扰动的共生模型，它的一些系数与时间有关。在一些假设下，我们努力证明正解的存在性和唯一性，并讨论了问题的渐近行为。此外，我们还证明了该系统的随机有界性、均匀连续性和随机持久性。最后，介绍了一些数值模拟来说明我们的主要结果。