Global bifurcations of limit cycles in a Holling-type dynamical system
Valery A. Gaiko
TL;DR
This paper provides a comprehensive analysis of a Holling-type predator-prey model, establishing that it can have at most two limit cycles around a singular point, enhancing understanding of its global bifurcation behavior.
Contribution
It offers the first complete global bifurcation analysis of a quartic Holling-type system, determining the maximum number of limit cycles possible.
Findings
The system can have at most two limit cycles.
Global bifurcation structure is fully characterized.
The analysis advances ecological modeling understanding.
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Differential Equations Analysis