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J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,” Applied Mathematical Sciences, Vol. 42, Springer Verlag, 2002.

has been cited by the following article:

• TITLE: Simultaneous Periodic Orbits Bifurcating from Two Zero-Hopf Equilibria in a Tritrophic Food Chain Model

  AUTHORS: Vctor Castellanos, Jaume Llibre, Ingrid Quilantan

  KEYWORDS: Periodic Orbit; Averaging Theory; Zero-Hopf Bifurcation; Population Dynamics

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.1 No.7, December 17, 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 zero-Hopf equilibrium points that the model has adequate values of its parameters. As far as we know, this is the first time that the phenomena appear in the literature related with food chain models.