In this paper, we consider a microorganism flocculation model with stochastic perturbation and time delay. By constructing some suitable Lyapunov functions, the asymptotic behaviors of the solution of the stochastic model around the equilibria of the corresponding deterministic model are investigated. We find that the average in time of the second moment of the solutions of the stochastic system is bounded to a relatively small noise.

中文翻译：

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时滞随机微生物絮凝模型的渐近行为

在本文中，我们考虑了具有随机扰动和时滞的微生物絮凝模型。通过构造一些合适的Lyapunov函数，研究了随机模型在相应确定性模型的平衡附近的解的渐近行为。我们发现，随机系统解的第二时刻的平均时间被限制在一个相对较小的噪声中。