Before revision:  More precisely, homeostasis refers to a phenomenon whereby the output x_o of a system is approximately constant on variation of an input I. Homeostatic phenomena are ubiquitous in biochemical networks of differential equations and these networks can be abstracted as digraphs G with a fixed input node \iota and a different fixed output node o . We assume that only the input node depends explicitly on \mathcal{I x_o(I) . We then study infinitesimal homeostasis :
After revision:  More precisely, homeostasis refers to a phenomenon whereby the output x_o of a system is approximately constant on variation of an input I. Homeostatic phenomena are ubiquitous in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs G with a fixed input node \iota and a different fixed output node o . We assume that only the input node depends explicitly on \mathcal{I x_o(I) . We then study infinitesimal homeostasis :