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

2015/04/13 by Valery A. Gaiko, Gaiko, Valery A.
Mathematics · #34C05 #34C07 #37G10 #37G15 #92D25 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:34C05 #msc:34C07 #msc:37G10 #msc:37G15 #msc:92D25

paper · pdf · doi:10.48550/arxiv.1504.03353

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

arxiv created 2015/07/27 · arxiv updated 2015/07/28

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.

Citations

• Global bifurcations of multiple limit cycles in the FitzHugh-Nagumo system
• Limit Cycle Bifurcations in a Quartic Ecological Model

Related

• Limit Cycle Bifurcations in a Quartic Ecological Model
• Four limit cycles in a predator-prey system of Leslie type with generalized Holling type III functional response
• Hopf Cyclicity and Global Dynamics for a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response
• Isola and mushroom dynamics of limit cycles and bifurcations in a predator-prey system with additive Allee effect
• Limit cycle bifurcations of a reduced Topp system