  Burstiness, the tendency of interaction events to be heterogeneously
distributed in time, is critical to information diffusion in physical and
social systems. However, an analytical framework capturing the effect of
burstiness on generic dynamics is lacking. We develop a master equation
formalism to study cascades on temporal networks with burstiness modelled by
renewal processes. Supported by numerical and data-driven simulations, we
describe the interplay between heterogeneous temporal interactions and models
of threshold-driven and epidemic spreading. We find that increasing interevent
time variance can both accelerate and decelerate spreading for threshold
models, but can only decelerate epidemic spreading. When accounting for the
skewness of different interevent time distributions, spreading times collapse
onto a universal curve. Our framework uncovers a deep yet subtle connection
between generic diffusion mechanisms and underlying temporal network structures
that impacts on a broad class of networked phenomena, from spin interactions to
epidemic contagion and language dynamics.
