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 : points \mathcal{I_0 where dx_o{d\mathcal{I}}(\mathcal{I}} _0. Stability implies that there is a stable equilibrium X(\mathcal{I})
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 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) _0 where dx_o{d\mathcal{I}}(\mathcal{I}} _0. Stability implies that there is a stable equilibrium X(\mathcal{I})