Global bifurcation analysis of Topp system

Valery A. Gaiko, Henk W. Broer, Alef E. Sterk

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Samenvatting

In this paper, we study the 3-dimensional Topp model for the dynamics of diabetes. First, we reduce the model to a planar quartic system. In particular, studying global bifurcations, we prove that such a system can have at most two limit cycles. Next, we study the dynamics of the full 3-dimensional model. We show that for suitable parameter values an equilibrium bifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests that near this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arise through period doubling cascades of limit cycles.
Originele taal-2English
Pagina's (van-tot)244–250
Aantal pagina's7
TijdschriftCybernetics and Physics
Volume8
Nummer van het tijdschrift4
DOI's
StatusPublished - dec.-2019

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