A prototype compartmental model of blood pressure distribution

We consider a system of differential equations, the behavior of whose solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling [R. Bellman, Mathematical Methods in Medicine, in: Series in Modern Applied Mathematics, vol. 1, World Scientific Publishing Co., Singapore, 1983; J.A. Jacquez, Compartmental Analysis in Biology and Medicine, Elsevier, New York, 1972] of the cardiovascular system. It admits a unique bounded solution such that all coordinates of the solution are separated from zero by positive numbers, and which is periodic, eventually periodic or almost periodic depending on the moments of heart contraction. Appropriate numerical simulations are provided. Some of the results were announced at The Fifth International Conference on Dynamic Systems and Applications held at Morehouse College, Atlanta, in 2007 [M.U. Akhmet, G. Bekmukhambetova, On modeling of blood pressure distribution, in: Proceedings of the Fifth International Conference on Dynamic Systems and Applications held at Morehouse College, Atlanta, USA, May 30–June 2, 2007, Proc. Dyn. Syst. Appl., 5 (2008) 17–20].