Global bifurcation analysis of Topp system

Abstract

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

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    Last time updated on 29/05/2021