Integrator Sensitivity of Chaos in the Ultradian Glucose-Insulin Model

Postgraduate and Research Department of Physics, St. Xavier’s College (Autonomous), Kolkata, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 29 May 2026

Abstract

Diabetes mellitus is a long-term metabolic disorder. It happens when the glucose-insulin system does not work properly. As a result, blood glucose levels are not well controlled. The ultradian model helps describe the main processes of this system. It includes nonlinear interactions, time delays, and feedback effects. Because of this, the model can represent both normal and diseased conditions. In this paper, the dynamical behavior of the glucose-insulin regulatory system is studied, incorporating periodic pulsatile forcing. We investigate the system using a range of numerical integrators and employ multiple chaotic indicators, including the Maximal Lyapunov Exponent and Fast Lyapunov Indicator, over a large number of kickrelaxation cycles to characterize its dynamical nature. Our results reveal that the choice of integrator and its computational efficiency play a crucial role in the observed behavior and the values of these chaotic indicators. Based on these non-trivial findings, we present a detailed initial analysis of this newly identified integrator-sensitive behavior, quantifying the performance and sensitivity of different integrators with respect to multiple chaotic indicators. This analysis will help us to understand the dynamics of the glucose-insulin regulatory system at a deeper level and thus enable the suggestion of possible cures for this widespread disease.