 Global qualitative analysis of a predator–prey system with Allee effect on the prey speciesJian Zu Mathematics and Computers in Simulation (MATCOM), 2013, vol. 94, issue C, 33-54 Abstract: In this paper, the Allee effect is incorporated into a predator–prey model with linear functional response. Compared with the predator–prey model without the Allee effect, it is found that the Allee effect of the prey species increases the extinction risk of both the prey and predator. If the Allee effect of the prey species is strong and the mortality of the predator species is relatively low, then the prey and predator cannot coexist after the predator invasion. Moreover, it is shown that the model with Allee effect undergoes the heteroclinic loop bifurcation and subcritical and supercritical Hopf bifurcations. With the brokenness of the heteroclinic loop, a stable or unstable limit cycle will appear. The Allee effect of the prey species can lead to unstable or stable periodic fluctuations. It is also found that the positive equilibrium of the model could change from stable to unstable, and then disappear when the strength of Allee effect increases continuously from zero. Keywords: Allee effect; Extinction threshold; Global bifurcation; Hopf bifurcation; Heteroclinic loop (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:94:y:2013:i:c:p:33-54 DOI: 10.1016/j.matcom.2013.05.009 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.