  We review modeling attempts for the paradigmatic contact process (or SIS
model) on adaptive networks. Elaborating on one particular proposed mechanism
of topology change (rewiring) and its mean field analysis, we obtain a
coarse-grained view of coevolving network topology in the stationary active
phase of the system. Introducing an alternative framework applicable to a wide
class of adaptive networks, active stationary states are detected, and an
extended description of the resulting steady-state statistics is given for
three different rewiring schemes. We find that slight modifications of the
standard rewiring rule can result in either minuscule or drastic change of
steady-state network topologies.
