Slow dynamics of the contact process on complex networks

TL;DR

This paper investigates slow dynamics in the contact process on complex networks, revealing Griffiths phases and rare region effects due to disorder and topology, with implications for propagation phenomena.

Contribution

It demonstrates that Griffiths phases can arise from topological heterogeneity alone, even without quenched disorder, in networks with finite topological dimension.

Findings

Griffiths phases observed in Erdős-Rényi networks due to disorder.

Slow relaxation phenomena linked to network topology.

Smeared phase transition in infinite size scale-free networks.

Abstract

The Contact Process has been studied on complex networks exhibiting different kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other rare region effects, in Erd\H os R\'enyi networks, leading rather generically to anomalously slow (algebraic, logarithmic,...) relaxation. More surprisingly, it turns out that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of sole topological heterogeneity in networks with finite topological dimension. In case of scale-free networks, exhibiting infinite topological dimension, slow dynamics can be observed on tree-like structures and a superimposed weight pattern. In the infinite size limit the correlated subspaces of vertices seem to cause a smeared phase transition. These results have a broad spectrum of implications for propagation phenomena and other dynamical process on networks and are relevant for the analysis of both models and empirical data.