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

Aguirre P.; Gonzalez-Olivares, E; Sáez E.

Abstract

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. © 2009 Society for Industrial and Applied Mathematics.

Más información

Título según WOS: THREE LIMIT CYCLES IN A LESLIE-GOWER PREDATOR-PREY MODEL WITH ADDITIVE ALLEE EFFECT
Título según SCOPUS: Three limit cycles in a leslie-gower predator-prey model with additive allee effect
Título de la Revista: SIAM JOURNAL ON APPLIED MATHEMATICS
Volumen: 69
Número: 5
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 2009
Página de inicio: 1244
Página final: 1262
Idioma: English
URL: http://epubs.siam.org/doi/abs/10.1137/070705210
DOI:

10.1137/070705210

Notas: ISI, SCOPUS