THE DYNAMICS OF A THREE-SPECIES FOOD CHAIN INTERACTION MODEL WITH MICHAELIS-MENTEN TYPE FUNCTIONAL RESPONSE

Abstract

In this paper, we study an ecological model with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Michaelis-Mententype functional response for predator and top predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviours of this model are investigated. The dynamical behaviour is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.