Reaction-diffusion processes on correlated and uncorrelated scale-free networks

Abstract

We compare reaction-diffusion processes of the $A+A\to 0$ type on scale-free networks created with either the configuration model or the uncorrelated configuration model. We show via simulations that except for the difference in the behavior of the two models, different results are observed within the same model when the minimum number of connections for a node varies from $k_{\rm min}=1$ to $k_{\rm min}=2$. This difference is attributed to the varying local properties of the two systems. In all cases we are able to identify a power law behavior of the density decay with time with an exponent $f>1$, considerably larger than its lattice counterpart.