Conference proceeding
Input-Output Networks, Singularity Theory, and Homeostasis
Advances in Dynamics, Optimization and Computation, pp.31-65
Studies in Systems, Decision and Control
07/21/2020
DOI: 10.1007/978-3-030-51264-4_2
Abstract
Homeostasis is a regulatory mechanism that keeps some specific variable close to a set value as other variables fluctuate, and is of particular interest in biochemical networks. We review and investigate a reformulation of homeostasis in which the system is represented as an input-output network, with two distinguished nodes ‘input’ and ‘output’, and the dynamics of the network determines the corresponding input-output function of the system. Interpreting homeostasis as an infinitesimal notion—namely, the derivative of the input-output function is zero at an isolated point—we apply methods from singularity theory to characterise homeostasis points in the input-output function. This approach, coupled to graph-theoretic ideas from combinatorial matrix theory, provides a systematic framework for calculating homeostasis points in models, classifying different types of homeostasis in input-output networks, and describing all small perturbations of the input-output function near a homeostasis point.
Details
- Title: Subtitle
- Input-Output Networks, Singularity Theory, and Homeostasis
- Creators
- Martin GolubitskyIan StewartFernando AntoneliZhengyuan HuangYangyang Wang
- Resource Type
- Conference proceeding
- Publication Details
- Advances in Dynamics, Optimization and Computation, pp.31-65
- Publisher
- Springer International Publishing; Cham
- Series
- Studies in Systems, Decision and Control
- DOI
- 10.1007/978-3-030-51264-4_2
- eISSN
- 2198-4190
- ISSN
- 2198-4182
- Language
- English
- Date published
- 07/21/2020
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9984065469702771
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