Reaction-diffusion processes and metapopulation models in heterogeneous networks

摘要

Dynamical reaction-diffusion processes and meta-population models arestandard modeling approaches for a wide variety of phenomena in which localquantities - such as density, potential and particles - diffuse and interactaccording to the physical laws. Here, we study the behavior of two basicreaction-diffusion processes ($B \to A$ and $A+B \to 2B$) defined on networkswith heterogeneous topology and no limit on the nodes' occupation number. Weinvestigate the effect of network topology on the basic properties of thesystem's phase diagram and find that the network heterogeneity sustains thereaction activity even in the limit of a vanishing density of particles,eventually suppressing the critical point in density driven phase transitions,whereas phase transition and critical points, independent of the particledensity, are not altered by topological fluctuations. This work lays out atheoretical and computational microscopic framework for the study of a widerange of realistic meta-populations models and agent-based models that includethe complex features of real world networks.