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Turkish Journal of Mathematics

Abstract

We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.

DOI

10.3906/mat-1411-8

Keywords

Predator-prey system, mate-finding Allee effect, nonmonotonic functional response, Bogdanov-Takens bifurcation, heteroclinic curve, homoclinic loop

First Page

585

Last Page

604

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