Broad lifetime distributions for ordering dynamics in complex networks

TL;DR

This paper investigates how large mesoscale heterogeneity in complex networks prevents the emergence of a characteristic time scale in ordering dynamics, leading to persistent metastable states.

Contribution

It demonstrates that mesoscale heterogeneity is sufficient to eliminate a characteristic ordering time in complex networks, highlighting the role of network structure in dynamics.

Findings

Heterogeneity at the mesoscale level prevents a characteristic ordering time.

Metastable states persist indefinitely in highly heterogeneous networks.

Large heterogeneity leads to the absence of a typical relaxation time.

Abstract

We search for conditions under which a characteristic time scale for ordering dynamics towards either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks with mesoscale community structure built up from randomly connected cliques. We find that large heterogeneity at the mesoscale level of the network appears to be a sufficient mechanism for the absence of a characteristic time for the dynamics. Such heterogeneity results in dynamical metastable states that survive at any time scale.