  We study deterministic systems, composed of excitable units of
FitzHugh-Nagumo type, that are capable of self-generating and self-terminating
strong deviations from their regular dynamics without the influence of noise or
parameter change. These deviations are rare, short-lasting, and recurrent and
can therefore be regarded as extreme events. Employing a range of methods we
analyze dynamical properties of the systems, identifying features in the
systems' dynamics that may qualify as precursors to extreme events. We
investigate these features and elucidate mechanisms that may be responsible for
the generation of the extreme events.
