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Delay equation analysis of human respiratory stability. (English) Zbl 0930.92006

Summary: A mathematical analysis of the stability in human respiration, based on the \(\tau\)-decomposition method, is conducted on a simple, but realistic \(\text{CO}_2\) model of the respiratory system. This model incorporates a two-compartment representation (lungs and tissues) for the plant and a very general class of controllers. 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 \(\text{CO}_2\) 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.

MSC:

92C30 Physiology (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K35 Control problems for functional-differential equations
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