Reaction-diffusion processes on correlated and uncorrelated scale-free networks

TL;DR

This paper investigates reaction-diffusion processes on scale-free networks, comparing different network models and node connectivity, revealing power-law decay behaviors with larger exponents than in lattice systems.

Contribution

It provides a comparative analysis of reaction-diffusion dynamics on correlated and uncorrelated scale-free networks, highlighting the impact of local network properties on decay behavior.

Findings

Power-law decay of density with exponent > 1

Differences in behavior between network models and minimum degree variations

Decay exponents larger than in lattice systems

Abstract

We compare reaction-diffusion processes of the $A+A\to 0$ type on scale-free networks created with either the configuration model or the uncorrelated configuration model. We show via simulations that except for the difference in the behavior of the two models, different results are observed within the same model when the minimum number of connections for a node varies from $k_{\rm min}=1$ to $k_{\rm min}=2$. This difference is attributed to the varying local properties of the two systems. In all cases we are able to identify a power law behavior of the density decay with time with an exponent $f>1$, considerably larger than its lattice counterpart.