Observational data suggest that periodic breathing is more common in subjects with low Fmath image, high apnoeic thresholds or high chemoreflex sensitivity. It is, however, difficult to determine the individual effect of each variable because they are intrinsically related. To distinguish the effect of isolated changes in chemoreflex sensitivity, mean Fmath image and apnoeic threshold, we employed a modelling approach to break their obligatory in vivo interrelationship. We found that a change in mean CO2 fraction from 0.035 to 0.045 increased loop gain by 70 ± 0.083% (P < 0.0001), irrespective of chemoreflex gain or apnoea threshold. A 100% increase in the chemoreflex gain (from 800 l min−1 (fraction CO2)−1) resulted in an increase in loop gain of 275 ± 6% (P < 0.0001) across a wide range of values of steady state CO2 and apnoea thresholds. Increasing the apnoea threshold Fmath image from 0.02 to 0.03 had no effect on system stability. Therefore, of the three variables the only two destabilizing factors were high gain and high mean CO2; the apnoea threshold did not independently influence system stability. Although our results support the idea that high chemoreflex gain destabilizes ventilatory control, there are two additional potentially controversial findings. First, it is high (rather than low) mean CO2 that favours instability. Second, high apnoea threshold itself does not create instability. Clinically the apnoea threshold appears important only because of its associations with the true determinants of stability: chemoreflex gain and mean CO2.