Abstract.
This paper has a dual purpose. First, we describe numerical methods for continuation and bifurcation analysis of steady state solutions and periodic solutions of systems of delay differential equations with an arbitrary number of fixed, discrete delays. Second, we demonstrate how these methods can be used to obtain insight into complex biological regulatory systems in which interactions occur with time delays: for this, we consider a system of two equations for the plasma glucose and insulin concentrations in a diabetic patient subject to a system of external assistance. The model has two delays: the technological delay of the external system, and the physiological delay of the patient's liver. We compute stability of the steady state solution as a function of two parameters, compare with analytical results and compute several branches of periodic solutions and their stability. These numerical results allow to infer two categories of diabetic patients for which the external system has different efficiency.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 6 October 1999 / Revised version: 15 August 2000 /¶Published online: 16 March 2001
Rights and permissions
About this article
Cite this article
Engelborghs, K., Lemaire, V., Bélair, J. et al. Numerical bifurcation analysis of delay differential equations arising from physiological modeling. J Math Biol 42, 361–385 (2001). https://doi.org/10.1007/s002850000072
Issue Date:
DOI: https://doi.org/10.1007/s002850000072