Author/Authors :
Sunaryo، Mada Sanjaya Waryano نويسنده Department of Mathematics, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu,Terengganu, Malaysia , , Mamat، Mustafa نويسنده Department of Mathematics, Faculty of Sciences and Technology, Universiti Malaysia Terengganu, 21030 K. Terengganu, Malaysia , , Salleh، Zabidin نويسنده Department of Mathematics, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu,Terengganu, Malaysia , , Mohd، Zakaria-Ismail نويسنده , , Mohamad Noor، Noor Maizura نويسنده Department of Computer Science, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu,Terengganu, Malaysia ,
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.
