Pattern formation and efficiency of reaction-diffusion processes on complex networks

Understanding how the topology of a network influences a given dynamics taking place on it is a major challenge in many fields of science. In this letter, we address part of this challenge by studying the impact of topological correlations in complex networks on the pattern formation and the efficiency of the reaction-diffusion process A + B -> empty set, the latter serving as a generic dynamics capturing the essentials of many real world examples. The major results are that i) the pattern formation can be characterized by a single scalar observable directly related to the amount of topological correlations and that, counterintuitively, ii) a large amount of pattern formation (i.e., of segregation of the two species A and B) does not necessarily mean a small efficiency, in contrast to regular d-dimensional lattices. Thus, particular topological correlations in complex networks allow for achieving opposing dynamical aims, as frequently observed in biological systems under opposing evolutionary pressures. Copyright (c) EPLA, 2008.