  Stochastic reaction-diffusion models can be analytically studied on complex
networks using the linear noise approximation. This is illustrated through the
use of a specific stochastic model, which displays traveling waves in its
deterministic limit. The role of stochastic fluctuations is investigated and
shown to drive the emergence of stochastic waves beyond the region of the
instability predicted from the deterministic theory. Simulations are performed
to test the theoretical results and are analyzed via a generalized Fourier
transform algorithm. This transform is defined using the eigenvectors of the
discrete Laplacian defined on the network. A peak in the numerical power
spectrum of the fluctuations is observed in quantitative agreement with the
theoretical predictions.
