Enregistré dans:
| Auteurs principaux: | , , , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2306.15145 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929513918627840 |
|---|---|
| author | Duncan, William Antoneli, Fernando Best, Janet Golubitsky, Martin Jin, Jiaxin Nijhout, H. Frederik Reed, Mike Stewart, Ian |
| author_facet | Duncan, William Antoneli, Fernando Best, Janet Golubitsky, Martin Jin, Jiaxin Nijhout, H. Frederik Reed, Mike Stewart, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15145 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homeostasis Patterns Duncan, William Antoneli, Fernando Best, Janet Golubitsky, Martin Jin, Jiaxin Nijhout, H. Frederik Reed, Mike Stewart, Ian Dynamical Systems 92B05, 37C20, 15A15 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. |
| title | Homeostasis Patterns |
| topic | Dynamical Systems 92B05, 37C20, 15A15 |
| url | https://arxiv.org/abs/2306.15145 |