Patterns of Homeostasis in Input-Output Networks

Steve Manns

Ohio State University

"Patterns of Homeostasis in Input-Output Networks"

Homeostasis is a regulatory mechanism by which a distinguished output variable remains approximately constant as an external input parameter varies over an interval. When perceived from a mathematical perspective, a natural interpretation of this phenomenon is that the derivative of the output variable with respect to the external input parameter vanishes. In the recent literature, this interpretation of homeostasis has been called 'infinitesimal homeostasis' and has the advantage that it allows one to apply results from singularity theory. While there are a variety of interesting questions one can try to answer using this theory, the question taken up in this project is: 'What can one say about which variables in a given network exhibit infinitesimal homeostasis along with the output variable?' Such questions relate to patterns of homeostasis in input-output networks, and our goal is to provide an answer based on rigorous mathematics.
Additional authors: Martin Golubitsky; Janet Best

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