Non-autonomous chemostat models with non-monotonic growth

In this paper, we investigate four non-autonomous chemostat models with non-monotonic consumption function, where wall growth and nutrient recycling are also taken into account. In each case, we prove the existence and uniqueness of non-negative global solution that generates a non-autonomous dynamical system. In addition, we also prove the existence of a unique (global) pullback attractor whose internal structure provides detailed information about the long-time behaviour of the state variables, for instance, conditions to ensure the extinction and the persistence of the species. We also display numerical simulations to illustrate the theoretical results.