Hopf Bifurcation of a Minimal Mathematical Model of Glucose-Insulin Kinetics

Harerimana Jean, Ntaganda Jean Marie

Abstract: This paper deals with Hopf bifurcation of the minimal mathematical model of glucose-insulin kinetics. This mathematical model consists of a system of nonlinear differential equations with time delays of the glucose-insulin. Different set of parameters used in order to match the real biological conditions. Numerical simulation are done using Matlab package. The results show that the critical delays periodic oscillations occurred and Hopf bifurcation has been token place at this level. For lower delays than critical the dynamical system deals with the stability while the values greater than critical delays it is unstable.

Keywords: Hopf bifurcation, Stable, Unstable, Linearization, Nonlinear differential equation, Characteristic equation, Critical delays.