Simultaneous periodic orbits bifurcating from two zero-Hopf equilibria in a tritrophic food chain model
Castellanos, Víctor (UJAT(México).Division Académica de Ciencias Básicas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Quilantán, Ingrid (UJAT(México).Division Académica de Ciencias Básicas)

Date:	2013
Abstract:	We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle and highest trophic species (first and second predator respectively). We prove that this model exhibits two small amplitud periodic solutions bifurcating simultaneously each one from one of the two zeroHopf equilibrium points that the model has for adequate values of its parameters. As far as we know this is the first time that this phenomena appear in the literature related with food chain models.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic orbit ; Averaging theory ; Zero-Hopf bifurcation ; Population dynamics
Published in:	Journal of Applied Mathematics and Physics, Vol. 1 (2013) , p. 31-38, ISSN 2327-4379

DOI: 10.4236/jamp.2013.17005

Postprint 13 p, 280.0 KB

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