Valery A. Gaiko
Published 2015-04-13Version 1
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global bifurcations, we prove that such a system can have at most two limit cycles surrounding one singular point.
Comments: 19 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1104.3019, arXiv:0902.2433
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Transversal conics and the existence of limit cycles
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