  Bursty dynamics of agents is shown to appear at criticality or in extended
Griffiths phases, even in case of Poisson processes. I provide numerical
evidence for power-law type of inter-communication time distributions by
simulating the Contact Process and the Susceptible-Infected-Susceptible model.
This observation suggests that in case of non-stationary bursty systems the
observed non-poissonian behavior can emerge as the consequence of an underlying
hidden poissonian network process, which is either critical or exhibits strong
rare-region effects. On contrary, in time varying networks rare-region effects
do not cause deviation from the mean-field behavior and heterogeneity induced
burstyness is absent.
