Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

This paper investigates the dynamics of a model two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove existence and uniqueness non-negative global solution as well compact absorbing attracting sets for solutions corresponding system. After that, we study internal structure set to obtain more detailed information about long-time behavior state variables. In such way, provide conditions under which extinction species cannot be avoided ensure persistence species, is often main goal pursued practitioners. addition, illustrate theoretical results several numerical simulations.