Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 164, pp. 1-14.

Title: Nonexistence of periodic orbits for predator-prey system
       with strong Allee effect in prey populations.
        
Authors: Jinfeng Wang (Harbin Normal Univ., Heilongjiang, China)
         Junping Shi  (College of William and Mary, Williamsburg, VA, USA)
         Junjie Wei   (Harbin Normal Univ., Heilongjiang, China)

Abstract:
 We use Dulac criterion to prove the nonexistence of periodic orbits
 for a class of general predator-prey system with strong Allee effect
 in the prey population growth. This completes the global bifurcation
 analysis of typical predator-prey systems with strong Allee effect
 for all possible parameters.

Submitted March 25, 2013. Published July 19, 2013.
Math Subject Classifications: 34C25, 34D23, 92D25.
Key Words: Predator-prey system; nonexistence of periodic orbits;
           Dulac criterion; global bifurcation.