ISSN 2094-2818

Editors: Eduardo A. Padlan and
Gisela P. Padilla-Concepcion
VOLUME 7 NUMBER 1 (January to June 2014)
 

Phil. Sci. Lett. 2014 7 (1) 67-72
available online: March 1, 2014

*Corresponding author
Email Address: jacollera@up.edu.ph
Received: November 4, 2013
Revised: January 24, 2014
Accepted: February 7, 2014
Published: March 1, 2014
Editor-in-charge: Eduardo R. Mendoza
Reviewers: Jose Maria L. Escaner IV and Eduardo R. Mendoza

Keywords: delay differential equations, gestation period, Hopf bifurcation, periodic solutions, predator-prey system, population dynamics, stability switch

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  ARTICLE
Stability switch and periodic solutions in delayed three-species model with Holling type III functional response


by Juancho A. Collera*

Department of Mathematics and Computer Science, University of the Philippines Baguio

In this paper, a system of delay differential equations that models two predator populations consuming a single prey population is considered. The prey population follows a logistic growth in the absence of predators while each of the predator populations has functional response of Holling type III. Each of these response terms includes a delay time which reflects the gestation period of the respective predator population. The positive equilibrium solution of the form (x, y, y) is called the symmetric equilibrium. This work examines the effects of the difference in gestation periods to the dynamical behaviour of the symmetric equilibrium. Conditions for stability and bifurcations of the symmetric equilibrium are given when the delay times are unequal. Numerical simulations are performed to illustrate stability switch and emergence of periodic solution through Hopf bifurcation.