In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system … with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction … and permanence of the system are established via the comparison theorem. Numerical simulations are carried out to explain …

attractive. The conditions of permanence are established by the method of comparison involving multiple Liapunov functions and …

. Conditions for the extinction of the prey and top predator are given. By using the Floquet theory of impulsive differential … periodic solution. Further, we obtain the conditions of permanence of the system. …

than some critical value, and a permanence condition is established via the method of comparison involving multiple …

that there is unique positive global solution. We establish the sufficient conditions for disease extinction. The … sufficient condition for disease persistence is also given. The basic reproduction number (R∗) of the deterministic system is …

conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer …

In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and …

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of … the chemostat. We establish the Fokker–Planck equation associated with this diffusion process, in particular we describe …