Global bifurcation analysis of Topp system
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.
CYBERNETICS AND PHYSICS, Vol. 8, Is. 4, 2019, 244–250, https://doi.org/10.35470/2226-4116-2019-8-4-244-250