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.