  Homeostasis occurs in a biological system when a chosen output variable
remains approximately constant despite changes in an input variable. In this
work we specifically focus on biological systems which may be represented as
chemical reaction networks and consider their infinitesimal homeostasis, where
the derivative of the input-output function is zero. The specific challenge of
chemical reaction networks is that they often obey various conservation laws
complicating the standard input-output analysis. We derive several results that
allow to verify the existence of infinitesimal homeostasis points both in the
absence of conservation and under conservation laws where conserved quantities
serve as input parameters. In particular, we introduce the notion of
infinitesimal concentration robustness, where the output variable remains
nearly constant despite fluctuations in the conserved quantities. We provide
several examples of chemical networks which illustrate our results both in
deterministic and stochastic settings.
