A new explicit stability criterion for human periodic breathing<--RID="*"--><--ID="*" This research was supported by grants from DRED (96-920).-->

The aim of this paper is to carry out a stability analysis for periodic breathing in humans that incorporates the dynamic characteristics of ventilation 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-dimensional non-linear delay differential system for which there exists a unique equilibrium point. Our stability analysis of this equilibrium point leads to the definition of a new explicit stability criterion and to the demonstration of the existence of a Hopf bifurcation. Numerical simulations illustrate the influence of physiological parameters on the stability of ventilation, and particularly the major role of the dynamic characteristics of the respiratory controller. Received: 2 February 1999 / Revised version: 18 June 1999 / Published online: 23 October 2000