Electron. J. Diff. Equ., Vol. 2013 (2013), No. 164, pp. 1-14.

Nonexistence of periodic orbits for predator-prey system with strong Allee effect in prey populations.

Jinfeng Wang, Junping Shi, Junjie Wei

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.

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Jinfeng Wang
School of Mathematical Science
Harbin Normal University
Harbin, Heilongjiang, 150025, China
email: jinfengwangmath@163.com
Junping Shi
Department of Mathematics, College of William and Mary
Williamsburg, VA 23187-8795, USA
email: shij@math.wm.edu
Junjie Wei
Department of Mathematics, Harbin Institute of Technology
Harbin, Heilongjiang, 150001, China
email: weijj@hit.edu.cn

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