Delay equation analysis of human respiratory stability

A mathematical analysis of the stability in human respiration, based on the τ-decomposition method, is conducted on a simple, but realistic CO2 model of the respiratory system. This model incorporates a two-compartment representation (lungs and tissues) for the plant and a very general class of controller. By deriving an explicit stability criterion, the stability domain of the respiratory system can be characterized. We quantify the influence of four major parameters of respiratory instability, i.e. transport delay, lung volume, and equilibrium values of lung CO2 partial pressure and controller gain. We demonstrate the existence of a bifurcation point and periodic solutions, giving some characteristics of solutions near the bifurcation point.