Dynamic behaviors for a model of predator-prey in the chemostat with microbial impulsive inputs

Abstract

In this paper, on the basis of the theories and methods of ecology and differential equations, a model of predator-prey in the chemostat with microbial impulsive inputs is established. By using the theories of impulsive equations, small amplitude perturbation skills and comparison techniques, we get the conditions which guarantee the globally asymptotical stability of the prey and predator eradication periodic solution. At the same time, we also prove that the system is permanent if some parameters satisfy certain conditions. Finally, some numerical simulations are carried out to illustrate the influences of impulsive inputs on the dynamic behaviors of system.