Simple Food Chain in a Chemostat with Distinct Removal Rates

In this paper, we consider a model describing predator-prey interactions in a chemostat that incorporates both general response functions and distinct removal rates. In this case, the conservation law fails. To overcome this difficulty, we make use of a novel way of constructing a Lyapunov function in the study of the global stability of a predator-free steady state. Local and global stability of other steady states, persistence analysis, as well as numerical simulations are also presented. Our findings are largely in line with those of an identical removal rate case.