IJPAM: Volume 89, No. 5 (2013)

MATHEMATICAL MODEL OF THREE SPECIES FOOD
CHAIN WITH HOLLING TYPE-III FUNCTIONAL RESPONSE

Mada Sanjaya Waryano Sunaryo$^1$, Zabidin Salleh$^2$, Mustafa Mamat$^3$
$^1$Department of Physics
Faculty of Science and Technology
Universitas Islam Negeri Sunan Gunung Djati
Bandung, INDONESIA
$^{2,3}$Department of Mathematics
Faculty of Science and Technology
Universiti Malaysia Terengganu
21030, Kuala Terengganu, Terengganu, MALAYSIA


Abstract. In this paper, we study ecological model with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III 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 behavior of this models 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.

Received: April 6, 2013

AMS Subject Classification: 34C23, 37G15, 37N25, 70K20,70K50

Key Words and Phrases: food chain model, Lotka-Volterra model, Holling type-III functional response, Hopf bifurcation

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DOI: 10.12732/ijpam.v89i5.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 5