Forward attractor for stochastic chemostat model with multiplicative noise

In this paper, we consider a stochastic chemostat model with multiplicative noise. By appropriate variable substitution, we get a random chemostat system driven by Ornstein-Uhlenbeck process, which will no longer contain white noise. Firstly, we prove the existence and uniqueness of the global positive solution for any positive initial value for random chemostat system. Secondly, we state some results regarding the existence of a compact forward absorbing set as well as a forward attracting one, its internal structure will provide us some useful information about the long-time behavior of microorganism in random chemostat model. Finally, we make some comparison and analysis between both ways of modeling randomness and stochasticity in the chemostat model and show some numerical simulations to support our theoretical results. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates a stochastic chemostat model with multiplicative noise, proving the existence and uniqueness of global positive solutions and discussing the impact of forward absorbing sets and forward attracting sets on the long-term behavior of microorganisms. Comparison between different ways of modeling randomness in the chemostat model is conducted, supported by numerical simulations.