Abstract

ESCOBAR CALLEJAS, Carlos Mario  and  GONZALEZ GRANADA, José Rodrigo. Hopf Bifurcation Dynamic in a Class of Competence Model Exhibiting Zip Bifurcation. Rev. ing. univ. Medellín [online]. 2011, vol.10, n.19, pp.159-169. ISSN 1692-3324.

This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator.

Keywords : Andrononov-Hopf bifurcation; Zip bifurcation; Lyapunov exponent.

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