Publications [#379662] of Michael C. Reed

Papers Published

1. Duncan, W; Antoneli, F; Best, J; Golubitsky, M; Jin, J; Nijhout, HF; Reed, M; Stewart, I, Homeostasis Patterns, SIAM Journal on Applied Dynamical Systems, vol. 23 no. 3 (January, 2024), pp. 2262-2292 [doi]
   (last updated on 2024/11/20)

   Abstract:
   Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distinguished input and output nodes, and the dynamics of the network determines the corresponding input-output function of the system. In this context, homeostasis can be defined as an ``infinitesimal"" notion, namely, the derivative of the input-output function is zero at an isolated point. Combining this approach with graph-theoretic ideas from combinatorial matrix theory provides a systematic framework for calculating homeostasis points in models and classifying the different homeostasis types in input-output networks. In this paper we extend this theory by introducing the notion of a homeostasis pattern, defined as a set of nodes, in addition to the output node, that are simultaneously infinitesimally homeostatic. We prove that each homeostasis type leads to a distinct homeostasis pattern. Moreover, we describe all homeostasis patterns supported by a given input-output network in terms of a combinatorial structure associated to the input-output network. We call this structure the homeostasis pattern network.