Slow, bursty dynamics as the consequence of quenched network topologies

Abstract

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.