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

Broad lifetime distributions for ordering dynamics in complex networks