  We study the robustness of the steady states of a class of systems of
autonomous ordinary differential equations (ODEs), having as a central example
those arising from (bio)chemical reaction networks. More precisely, we study
under what conditions the steady states of the system are contained in a
parallel translate of a coordinate hyperplane.
  To this end, we focus mainly on ODEs consisting of generalized polynomials,
and make use of algebraic and geometric tools to relate the local and global
structure of the set of steady states. Specifically, we consider the local
property termed zero sensitivity at a coordinate $x_i$, which means that the
tangent space is contained in a hyperplane of the form $x_i=c$, and provide a
criterion to identify it. We consider the global property termed absolute
concentration robustness (ACR), meaning that all steady states are contained in
a hyperplane of the form $x_i=c$.
  We clarify and formalise the relation between the two approaches. In
particular, we show that ACR implies zero sensitivity, and identify when the
two properties do not agree, via an intermediate property we term local ACR.
For families of systems arising from modelling biochemical reaction networks,
we obtain the first practical and automated criterion to decide upon (local)
ACR.
