Numerical Simulation Dynamical Model of Three Species Food Chain with Holling Type-II 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 Holling type-II functional response for predator and superpredator. 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 behaviors of this model are investigated. The dynamical behavior 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.