  Dynamical reaction-diffusion processes and meta-population models are
standard modeling approaches for a wide variety of phenomena in which local
quantities - such as density, potential and particles - diffuse and interact
according to the physical laws. Here, we study the behavior of two basic
reaction-diffusion processes ($B \to A$ and $A+B \to 2B$) defined on networks
with heterogeneous topology and no limit on the nodes' occupation number. We
investigate the effect of network topology on the basic properties of the
system's phase diagram and find that the network heterogeneity sustains the
reaction 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 particle
density, are not altered by topological fluctuations. This work lays out a
theoretical and computational microscopic framework for the study of a wide
range of realistic meta-populations models and agent-based models that include
the complex features of real world networks.
