This work focuses on studying high-codimensional bifurcations in the glucose model with
obesity’s effect. We examine the related dynamical behaviors, taking into account the
risk and adverse health effects associated with obesity’s impact on the glucose model.
Through the application of the normal form method, we demonstrate that the model
exhibits codimension-1 and codimension-2 bifurcations such as saddle node bifurcation
and cusp bifurcation. Additionally, we introduce and prove a theorem that establishes
the presence of Hopf bifurcation in the model. The computation of the first Lyapunov
coefficient is achieved using center manifold theory. To support our theoretical analysis
and showcase the model’s complex dynamical behaviors, including periodic curve families,
we provide numerical simulations. These simulations contribute to understanding
clinical observations regarding the effects of obesity on glucose levels, oscillations and
disorders. Ultimately, this research can aid in the early control of blood glucose levels.