Abstract
The object of this paper is to study the two parallel food chains model. We show that the dynamic outcomes of this model are sensitive to parameter values and initial data. There are several possible outcomes as follows: 1) Both predator and prey go extinct; 2) only the prey species survive; 3) predator and prey coexist in the form of equilibrium;4) predator and prey coexist in the form of oscillation. We analyze the case (1) ~ (3) rigorously. For the case (4), we do numerical simulations to describe all possible phenomena.