Codimension-1,2 bifurcation analysis of glucose model with obesity effect

Abstract

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.