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arXiv · 2306.15145

Homeostasis Patterns

William Duncan·Fernando Antoneli·Janet Best·Martin Golubitsky·Jiaxin Jin·H. Frederik Nijhout·Mike Reed·Ian Stewart
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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.

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William Duncan, Fernando Antoneli, Janet Best, Martin Golubitsky, Jiaxin Jin, H. Frederik Nijhout, Mike Reed, Ian Stewart. 2023-06-27. Homeostasis Patterns. https://doi.org/10.1137/23m158807x

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