THREE LIMIT CYCLES IN A LESLIE-GOWER PREDATOR-PREY MODEL WITH ADDITIVE ALLEE EFFECT

被引:136
作者
Aguirre, Pablo [1 ]
Gonzalez-Olivares, Eduardo [2 ]
Saez, Eduardo [1 ]
机构
[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile
[2] Pontificia Univ Catolica Valparaiso, Inst Matemat, Valparaiso, Chile
关键词
stability; limit cycles; homoclinic orbits; bifurcations; predator-prey models; Allee effect; BIFURCATIONS; SYSTEM; DYNAMICS;
D O I
10.1137/070705210
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, a bidimensional continuous-time differential equations system is analyzed which is derived of Leslie-type predator-prey schemes by considering a nonmonotonic functional response and Allee effect on population prey. For the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant, the only quadrant of interest for the sake of realism. We show that, under certain conditions over the parameters, the system allows the existence of three limit cycles: The first two cycles are infinitesimal ones generated by Hopf bifurcation; the third one arises from a homoclinic bifurcation. Furthermore, we give conditions over the parameters such that the model allows long-term extinction or survival of both populations. In particular, the presence of a weak Allee effect does not imply extinction of populations necessarily for our model.
引用
收藏
页码:1244 / 1262
页数:19
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