The impact of Allee effect on a predator–prey system with Holling type II functional response

In this paper, the Allee effect is incorporated into a predator–prey model with Holling type II functional response. Compared with the predator–prey model without Allee effect, we find that the Allee effect of prey species increases the extinction risk of both predators and prey. When the handling t...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 217; no. 7; pp. 3542 - 3556
Main Authors Zu, Jian, Mimura, Masayasu
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.2010
Elsevier
Subjects
Exact sciences and technology
Extinction risk
Handling
Heteroclinic cycle
Hopf bifurcation
Limit cycle
Materials handling
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Oscillations
Positive interactions
Predators
Sciences and techniques of general use
Stability switches
Steady state
Switches
Heteroclinic cycle
Positive interactions
Limit cycle
Stability switches
Extinction risk
Numerical analysis
Applied mathematics
Oscillation
Predator prey system
Hopf bifurcation
Steady state
Numerical stability
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Summary:In this paper, the Allee effect is incorporated into a predator–prey model with Holling type II functional response. Compared with the predator–prey model without Allee effect, we find that the Allee effect of prey species increases the extinction risk of both predators and prey. When the handling time of predators is relatively short and the Allee effect of prey species becomes strong, both predators and prey may become extinct. Moreover, it is shown that the model with Allee effect undergoes the Hopf bifurcation and heteroclinic bifurcation. The Allee effect of prey species can lead to unstable periodical oscillation. It is also found that the positive equilibrium of the model could change from stable to unstable, and then to stable when the strength of Allee effect or the handling time of predators increases continuously from zero, that is, the model admits stability switches as a parameter changes. When the Allee effect of prey species becomes strong, longer handling time of predators may stabilize the coexistent steady state.
Bibliography:ObjectType-Article-1
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.09.029