Ordering dynamics with two non-excluding options: the effects of community structure in language competition models

In the general context of dynamics of social consensus, we study an
agent based model for the competition between two socially equivalent
languages. 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. For this, 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.