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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

On the number of limit cycles in a predator prey model with non-monotonic functional response

Pages: 525 - 534, Volume 6, Issue 3, May 2006      doi:10.3934/dcdsb.2006.6.525

 
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E. González-Olivares - Instituto de Matemáticas, Grupo de Ecología Matemática, Pontificia Universidad Católica de Valparaíso. Casilla 4059, Valparaíso, Chile (email)
B. González-Yañez - Instituto de Matemáticas, Grupo de Ecología Matemática, Pontificia Universidad Católica de Valparaíso. Casilla 4059, Valparaíso, Chile (email)
Eduardo Sáez - Universidad Técnica Federico Santa María, Departamento de Matemática, Casilla 110-V, Valparaíso, Chile (email)
I. Szántó - Departamento de Matemáticas, Universidad Técnica Federico Santa María, Valparaíso, Chile (email)

Abstract: In this work we analyze a Gause type predator-prey model with a non-monotonic functional response and we show that it has two limit cycles encircling an unique singularity at the interior of the first quadrant, the innermost unstable and the outermost stable, completing the results obtained in previous paper [12, 17, 26, 28].
    Moreover, using the Poisson bracket we give a proof, shorter than the ones found in the literature, for determining the type of a cusp point of a singularity at the first quadrant.

Keywords:  predator-prey models, bifurcations, stability.
Mathematics Subject Classification:  92D25, 34C, 58F14, 58F21.

Received: August 2004;      Revised: December 2005;      Available Online: February 2006.