## Chapter 19

### Chemosensory respiratory control

The respiratory process is described, and the Grodins compartmental
model for the gas exchange of carbon dioxide and oxygen between the
lungs, arteries, brain and tissues is described. This is essentially a
set of first order ordinary differential equations, with a number of
delays due to transport of blood between the various
compartments. Even in dimensionless form, there are over a
*hundred* dimensionless parameters, and it is possible (and
necessary) to chart an asymptotic path through the model, reducing it
to several simpler forms. The most simple of these is a first order
delay differential equation of delay/recruitment type, and this is
analysed as the delay increases through the usual path from stable
steady state, to periodic oscillations, and then chaos.
In the notes, I discuss the problem of how to relate chaos in the
delay differential equation to that in the underlying difference
equation. There are some clues of what to do, but essentially I view
this as an unresolved problem.