A new explicit stability criterion for human periodic breathing

The aim of this paper is to carry out a stability analysis for periodic bre athing in humans that incorporates the dynamic characteristics of ventilati on control. A simple CO2 model that takes into account the main elements of the respiratory system, i.e. the lungs and the ventilatory controller with its dynamic properties, is presented. This model results in a three-dimens ional non-linear delay differential system for which there exists a unique equilibrium point. Our stability analysis of this equilibrium point lends t o the definition of a new explicit stability criterion and to the demonstra tion of the existence of a Hopf bifurcation. Numerical simulations illustra te the influence of physiological parameters on the stability of ventilatio n, and particularly the major role of the dynamic characteristics of the re spiratory controller.