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

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 H...

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Bibliographic Details
Authors: Llibre, Jaume|||0000-0002-9511-5999, Vidal, Claudio|||0000-0002-1630-0898
Format: article
Publication Date:2016
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:169494
Online Access:https://ddd.uab.cat/record/169494
https://dx.doi.org/urn:doi:10.3934/dcdsb.2016026
Access Level:Open access
Keyword:Averaging theory
Hopf bifurcation
Predator-prey model
Ratio-dependence
Description
Summary: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.