  Intermittent large amplitude events are seen in the temporal evolution of a
state variable of many dynamical systems. Such intermittent large events
suddenly start appearing in dynamical systems at a critical value of a system
parameter and continues for a range of parameter values. Three important
processes of instabilities, namely, interior crisis, Pomeau-Manneville
intermittency and the breakdown of quasiperiodic motion, are most common as
observed in many systems that lead to such occasional and rare transitions to
large amplitude spiking events. We characterize these occasional large events
as extreme events if they are larger than a statistically defined significant
height. We present two exemplary systems, a single system and a coupled system
to illustrate how the instabilities work to originate as extreme events and
they manifest as non-trivial dynamical events. We illustrate the dynamical and
statistical properties of such events.
