Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)

Date:	2016
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.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 316339
Note:	Agraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/R.
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Document:	Article
Subject:	Averaging theory ; Hopf bifurcation ; Predator-prey model ; Ratio-dependence
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 21 Núm. 6 (2016), p. 1859-1867, ISSN 1553-524X

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