  Known by many names and arising in many settings, the forced linear diffusion
model is central to the modeling of power and influence within social networks
(while also serving as the mechanistic justification for the widely used
spatial/network autocorrelation models). The standard equilibrium solution to
the diffusion model depends on strict timescale separation between network
dynamics and attribute dynamics, such that the diffusion network can be
considered fixed with respect to the diffusion process. Here, we consider a
relaxation of this assumption, in which the network changes only slowly
relative to the diffusion dynamics. In this case, we show that one can obtain a
perturbative solution to the diffusion model, which depends on knowledge of
past states in only a minimal way.
