Limit Cycle Bifurcations in a Quartic Ecological Model
Henk W. Broer, Valery A. Gaiko
TL;DR
This paper provides a comprehensive analysis of a quartic ecological model, establishing that the system can have at most two limit cycles through the study of bifurcations and singular points.
Contribution
It completes the global qualitative analysis of the model, specifically proving the maximum number of limit cycles is two.
Findings
The system has at most two limit cycles.
Global bifurcations of singular points are characterized.
The qualitative behavior of the ecological model is fully described.
Abstract
In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit cycles.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematical and Theoretical Epidemiology and Ecology Models · Quantum chaos and dynamical systems