Numerical Simulation Dynamical Model of Three Species Food Chain with Holling Type-II Functional Response

Waryano Sunaryo, Mada Sanjaya and Mamat, Mustafa and Salleh, Zabidin and Ismail, Mohd and Mohamad Noor, Noor Maizura (2011) Numerical Simulation Dynamical Model of Three Species Food Chain with Holling Type-II Functional Response. Malaysian Journal of Mathematical Sciences, 5 (1). pp. 1-12. ISSN 1823-8343

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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.

Item Type:Article
Keyword:Food chain model, Lotka-Volterra model, Holling type-II functional response, Hopf bifurcation
Faculty or Institute:Institute for Mathematical Research
Publisher:UPM Press
ID Code:12540
Deposited By: Najwani Amir Sariffudin
Deposited On:01 Jun 2011 08:34
Last Modified:27 May 2013 07:52

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