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We study the dynamics of the contact-process, one of the simplestnonequilibrium stochastic processes, taking place on a scale-free network. Weconsider the network topology as annealed, i.e. all links are rewired at eachmicroscopic time step, so that no dynamical correlation can build up. This is apractical implementation of the absence of correlations assumed by mean-fieldapproaches. We present a detailed analysis of the contact process in terms of aLangevin equation, including explicitly the effects of stochastic fluctuationsin the number of particles in finite networks. This allows us to determineanalytically the survival time for spreading experiments and the density ofactive sites in surviving runs. The fluctuations in the topological structureinduce anomalous scaling effects with respect to the system size when thedegree distribution has an "hard" upper bound. When the upper bound is soft,the presence of outliers with huge connectivity perturbs the picture even more,inducing an apparent shift of the critical point. In light of these findings,recent theoretical and numerical results in the literature are criticallyreviewed.

Langevin approach for the dynamics of the contact process on annealed scale-free networks