In this paper, we first construct a microfluidic chemostat model for the growth of biofilms and planktonic populations with random dilution ratios and then investigate its dynamical behavior. Using the theory of monotone dynamical systems and the Multiplicative Ergodic Theorem, we show the existence of random attractors and stationary measures, and present Lyapunov exponents for the linearized cocycle with respect to the random model. Further on, if the top Lyapunov exponent is negative, we give the extinction of microbial populations, including the forward and pull-back trajectories.

中文翻译：

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具有随机稀释比的微流体恒化器模型分析

在本文中，我们首先构建了一个微流体恒化器模型，用于生物膜和浮游生物种群的生长，具有随机稀释比，然后研究其动力学行为。利用单调动力系统理论和乘法遍历定理，我们证明了随机吸引子和稳态测度的存在性，并给出了线性化余循环相对于随机模型的李雅普诺夫指数。此外，如果李雅普诺夫最高指数为负，我们给出微生物种群的灭绝，包括前向和后退轨迹。