Forward attractor for stochastic chemostat model with multiplicative noise

Abstract

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.