= Delayed carbon-dioxide ventilation feedback
{title2=$K\dot P=M-PG[P(t-\tau)-P_0]_+$}
A one-compartment <carbon dioxide>[carbon-dioxide] balance couples metabolic production with pressure-dependent ventilatory removal. A <positive part>[positive-part] response models a nonnegative threshold-linear respiratory drive, and a transport/response delay can destabilize <negative feedback>. With $T=t/\tau$, $P=P_0+[M/(GP_0)]p$, the scaled law is $p'=\alpha[1-(1+\mu p)[p(T-1)]_+]$, where $\alpha=\tau GP_0/K$ and $\mu=M/(GP_0^2)$. Its positive <equilibrium> is $2/[1+\sqrt{1+4\mu}]$; $1/(1+\mu)$ is only its first-order small-$\mu$ approximation.
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