English

Global bifurcations of limit cycles in a Holling-type dynamical system

Dynamical Systems 2015-07-28 v2 Classical Analysis and ODEs

Abstract

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.

Keywords

Cite

@article{arxiv.1504.03353,
  title  = {Global bifurcations of limit cycles in a Holling-type dynamical system},
  author = {Valery A. Gaiko},
  journal= {arXiv preprint arXiv:1504.03353},
  year   = {2015}
}

Comments

19 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1104.3019, arXiv:0902.2433