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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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Vidal, Claudio|||0000-0002-1630-0898
Tipo de documento: artigo
Data de publicação:2016
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:169494
Acesso em linha:https://ddd.uab.cat/record/169494
https://dx.doi.org/urn:doi:10.3934/dcdsb.2016026
Access Level:Acceso aberto
Palavra-chave:Averaging theory
Hopf bifurcation
Predator-prey model
Ratio-dependence
Descrição
Resumo: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.