M. Golubitsky, I. Stewart, J. Best, H.F. Nijhout and M. Reed
Homeostasis with multiple inputs
Preprint. To appear.
The main focus in Golubitsky and Stewart was on systems with one input and one output variable, classified by a subfamily of the elementary catastrophes of and Zeeman. In this paper we use the singularity theory approach to study simultaneous homeostasis for two input parameters. As before, coordinate changes that preserve homeostasis play a prominent role because such coordinate changes provide the basis for singularity theory. We classify the singularities concerned and discuss their effect on homeostasis. We also speculate on why homeostasis in models may look as though it comes from infinitesimal homeostasis, even when technically it does not. This speculation uses the classification of elementary catastrophes.