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BIFURCATIONS OF A PREDATOR-PREY SYSTEM WITH WEAK ALLEE EFFECTS
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 Title & Authors
BIFURCATIONS OF A PREDATOR-PREY SYSTEM WITH WEAK ALLEE EFFECTS
Lin, Rongzhen; Liu, Shengqiang; Lai, Xiaohong;
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 Abstract
We formulate and study a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), no. 4, 1445-1472] but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).
 Keywords
predator-prey;weak Allee effects;bifurcation;limit cycle;
 Language
English
 Cited by
1.
Detecting the presence of depensation in collapsed fisheries: The case of the Northern cod stock, Ecological Economics, 2014, 97, 101  crossref(new windwow)
2.
A Simple Predator-Prey Population Model with Rich Dynamics, Applied Sciences, 2016, 6, 5, 151  crossref(new windwow)
3.
Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
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