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Zbl 1160.92038
Aguirre, Pablo; González-Olivares, Eduardo; Sáez, Eduardo
Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 3, 1401-1416 (2009). ISSN 1468-1218

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 2000:: *92D40 Ecology
34C05 Qualitative theory of some special solutions of ODE
34C23 Bifurcation (periodic solutions)

Keywords: stability; limit cycles; bifurcations; predator-prey models; Allee effect

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Zentralblatt MATH Berlin [Germany]