Communications in Mathematical Analysis
  • Year: 2006
  • Volume: 1
  • Issue: 1

Existence of Limit Cycles in a Predator-Prey System With a Functional Response of the Form Arctan(ax)

  • Author:
  • Basem S. Attili1, Saed F. Mallak2
  • Total Page Count: 8
  • Page Number: 33 to 40

1Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 17551, AlAin, United Arab Emirates, E-mail: b.attili@uaeu.ac.ae

2Department of mathematics, Arab American University at Jenin – Palestine, E-mail: smallak@ aauj.edu

(Communicated by Toka Diagana)

Abstract

We consider a predator prey system with the functional response of the form θ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of limit cycles for such system. A necessary and sufficient condition for the nonexistence of limit cycles is given for such system.

Keywords

Predator prey system, limit cycle, functional response