= Solution
The <positive part>[positive-part] law $\mathcal V(P)=G[P-P_0]_+$ is a threshold-linear approximation to the ventilatory response. Below the apnoeic threshold $P_0$, this model assigns zero <pulmonary ventilation>[ventilation]; above it, each <pressure> increment produces a proportional <pulmonary ventilation>[ventilation] increase, with gain $G>0$. Taking the <positive part> ensures a nonnegative <pulmonary ventilation>[ventilation] rate rather than the unphysical negative rate that unrestricted linear extrapolation would give. It is a local idealization of the response, not a claim that actual physiology lacks other respiratory drives or saturates nowhere. In the delayed model this response is evaluated at the delayed <pressure>.
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