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Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect. (English) Zbl 1160.92038
Summary: A bidimensional continuous-time differential equations system is analyzed which is derived from Leslie type predator-prey schemes by considering a nonmonotonic functional response and Allee effects on the prey population. For ecological reason, we describe the bifurcation diagram of limit cycles that appear only at the first quadrant in the system obtained. We also show that under certain conditions on the parameters the system allows the existence of a stable limit cycle surrounding an unstable limit cycle generated by Hopf bifurcations. Furthermore, we give conditions on the parameters such that the model allows long-term extinction or survival of both populations.

MSC:
92D40 Ecology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
Software:
Mathematica
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