IJPAM: Volume 47, No. 1 (2008)
THE DYNAMICS OF A TRI-TROPHIC FOOD
CHAIN IN THE CHEMOSTAT
CHAIN IN THE CHEMOSTAT
Sarah A. Al-Sheikh
Department of Mathematics
College of Science
King Abdulaziz University
P.O. Box 1454, Jeddah, 21431, KINGDOM OF SAUDI ARABIA
e-mail: salsheikh@kau.edu.sa
Department of Mathematics
College of Science
King Abdulaziz University
P.O. Box 1454, Jeddah, 21431, KINGDOM OF SAUDI ARABIA
e-mail: salsheikh@kau.edu.sa
Abstract.A tri-trophic food chain in the chemostat is studied and analyzed. The Michaelis-Menten functional response is used for all trophic levels. It is shown that the basic reproductive numbers of the prey and predator affect the dynamics of this model. Also using the dilution rate of the chemostat as a bifurcation parameter it is shown that the model undergoes a sequence of Hopf bifurcations.
Received: May 9, 2008
AMS Subject Classification: 92A11
Key Words and Phrases: food chain, tri-trophic, chemostat, global stability, Hopf bifurcation, dissipative, Dulac criterion, Liapunov function
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 1
