International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 377-385

Existence of limit cycles in a predator-prey system with a functional response

Basem S. Attili

Mathematical Sciences Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 16 January 2001

Copyright © 2001 Basem S. Attili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the existence of limit cycles for a predator-prey system with a functional response. The system has two or more parameters that represent the intrinsic rate of the predator population. A necessary and sufficient condition for the uniqueness of limit cycles in this system is presented. Such result will usually lead to a bifurcation curve.