  Self-exciting point processes describe the manner in which every event
facilitates the occurrence of succeeding events. By increasing excitability,
the event occurrences start to exhibit bursts even in the absence of external
stimuli. We revealed that the transition is uniquely determined by the average
number of events added by a single event, $1-1/\sqrt{2} \approx 0.2929$,
independently of the temporal excitation profile. We further extended the
theory to multi-dimensional processes, to be able to incite or inhibit bursting
in networks of agents.
