Forward dynamics and memory effect in a fractional order chemostat minimal model with non-monotonic growth

This paper aims to study the long-time dynamics of chemostat model with non-monotonic growth, subject to random bounded disturbances on the input flow.To be precise, we first prove existence and uniqueness of global positive solution of such model and then construct the compact forward absorbing and attracting sets, which are independent of the realizations of the input noise.Moreover, we prove the conditions for biomass extinction and species persistence.In particular, fractional operator has a noticeable effect, in such a way that it can delay the rate of extinction and persistence and amplitude of oscillator.Numerical simulations are presented to verify the theoretical results.