Stability of the Human Respiratory Control System. Part I: Analysis of a two-dimensional delay state-space model

Anumber of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing #including Cheyne-Stokes respiration and apneustic breathing# is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's #12#. The purpose of this paper is to study the stabilitycharacteristics of a feedback control system of #ve di#erential equations with delays in both the state and control variables presented by Khoo et al. #17# in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simpli#ed mathematical model of two nonlinear state equations modeling arterial partial pressures of O 2 and CO 2 and a peripheral controller. Analy..