  We consider steady states of dynamics that have an underlying network
structure. We study how a steady state responds to small perturbations in the
network parameters and how this sensitivity is connected to the network
structure. We introduce a prototypical linear response equation and determine
its sensitivity. This abstract result is applied to study the sensitivity of
steady states in two common dynamics on networks: continuous-time Markov chains
and deterministically modelled chemical reaction networks. For continuous-time
Markov chains, we are able to efficiently compute the signs of the response in
terms of the underlying network structure. The study of chemical reaction
networks extends the sensitivity analysis to open systems with more complex
network structures.
