Analysis of Glucose, Insulin, Epinephrine Dynamics Using Multidimensional Ostrowski-Type Inequality

This paper presents a comprehensive stability analysis of a three-dimensional dynamical system that models glucose–insulin interactions with epinephrine as a third regulatory variable. The system captures the dynamics of glucose concentration (g), insulin concentration (h), and epinephrine levels (e), incorporating the influence of external perturbations represented by J(t), P(t), and Z(t). By applying multidimensional Ostrowski-type inequalities, we establish global stability criteria, derive sharp bounds on system trajectories, and provide a theoretical basis for clinical decision-making in diabetes management. The proposed framework allows for precise quantification of deviation bounds and convergence rates.