  The recent availability of huge high resolution datasets on human activities
has revealed the heavy-tailed nature of the interevent time distributions. In
social simulations of interacting agents the standard approach has been to use
Poisson processes to update the state of the agents, which gives rise to very
homogeneous activity patterns with a well defined characteristic interevent
time. As a paradigmatic opinion model we investigate the voter model and review
the standard update rules and propose two new update rules which are able to
account for heterogeneous activity patterns. For the new update rules each node
gets updated with a probability that depends on the time since the last event
of the node, where an event can be an update attempt (exogenous update) or a
change of state (endogenous update). We find that both update rules can give
rise to power law interevent time distributions, although the endogenous one
more robustly. Apart from that for the exogenous update rule and the standard
update rules the voter model does not reach consensus in the infinite size
limit, while for the endogenous update there exist a coarsening process that
drives the system toward consensus configurations.
