Numerical simulation dynamical model of three-species food chain with Lotka-Volterra linear functional response

In this paper, we study an ecological model with a tritrophic food chain with a classical Lotka-Volterra functional response. There are three equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the 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. It has been found that the extinction of the predator depends on the prey-predator parameter in the equation. The dynamical behaviour is found to be very sensitive to the parameter values and the initial condition as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings