Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure

Jaume Llibre; Claudio Vidal

doi:https://doi.org/10.3934/dcdsb.2016026

Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure

Jaume Llibre, Claudio Vidal

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

A ratio-dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small-amplitude Hopf limit cycles being the equilibrium point E∗ unstable.

Original language	English
Pages (from-to)	1859-1867
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	21
Issue number	6
DOIs	https://doi.org/10.3934/dcdsb.2016026
Publication status	Published - 1 Aug 2016

Keywords

Averaging theory
Hopf bifurcation
Predator-prey model
Ratio-dependence

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abstract = "A ratio-dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small-amplitude Hopf limit cycles being the equilibrium point E∗ unstable.",

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