Diffusion-annihilation processes in complex networks
Rights accessOpen Access
We present a detailed analytical study of the A+A¿/0 diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of A particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e., a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.
CitationCatanzaro, M., Boguña, M., Pastor-Satorras, R. Diffusion-annihilation processes in complex networks. "Physical review E: statistical, nonlinear, and soft matter physics", 10 Maig 2005, vol. 71, núm. 5, p. 056104-1-056104-9.