Reaction-diffusion processes and metapopulation models in heterogeneous networks

TL;DR

This paper explores how network heterogeneity influences reaction-diffusion processes and phase transitions in metapopulation models, revealing that topology can sustain activity at low densities and alter critical points.

Contribution

It provides a theoretical and computational framework for analyzing reaction-diffusion and metapopulation models on complex networks, highlighting the impact of topology on phase behavior.

Findings

Heterogeneity sustains reaction activity at low densities.

Critical points are suppressed by network heterogeneity.

Phase transition properties are unaffected by topological fluctuations.

Abstract

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.