Zero-Hopf bifurcation in a predator-prey model
Falconi, Manuel (UNAM(México). Departamento de Matemáticas)
Gonzalez-Olivares, Eduardo (UNAM(México). Departamento de Matemáticas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	We study the competition between two species according the following modification of the Holling-Tanner II model x'= x[r(1 −x/K)−qy/x2 + a], y' = sy (1 −y/nx + c). Of course, x ≥ 0, y ≥ 0 and the parameters a, c, K, n, q, r and s are positive. We prove that its unique positive equilibrium point never exhibits a classical Hopf bifurcation, but for convenient values of the parameters from this equilibrium point bifurcates a periodic orbit, and during this local bifurcation the eigenvalues of such equilibrium remain purely imaginary.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments/Ajudes: The first author is partially supported by PAPIIT (IN111410)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Zero-Hopf bifurcation ; Predator-prey model
Published in:	Scientiae Mathematicae Japonicae, Vol. 76 Núm. 1 (2013) , p. 119-127, ISSN 1346-0447

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