  Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of
riddled basins of attraction in delay-coupled systems as the coupling between
the units is increased. We characterize the riddled basin using the uncertainty
exponent which is a measure of the dimensions of the basin boundary.
Additionally, we show that the phase space can be partitioned into pure and
mixed regions, where initial conditions in the pure regions certainly avoid the
generation of extreme events while initial conditions in the mixed region may
or may not exhibit such events. This implies, that any tiny perturbation of
initial conditions in the mixed region could yield the emergence of extreme
events because the latter state possesses a riddled basin of attraction.
