  In practical combustion systems, the high nonlinearity of the turbulent
combustion process can result in unexpected behavior even for nominal operating
conditions. This includes flame flashback in premixed gas turbines, engine
unstart in scramjets, and failure of engines to ignite at high altitudes. Many
of these events have catastrophic consequences. Hence, understanding the nature
of such irregular excursions of combustion systems is important to ensure
robust operation. The focus of this work is to identify the sources of such
rare excursions from a dynamical systems perspective. Specifically, such
anomalous behavior can be explained in terms of three different classes based
on the trajectories that the system traverses in its phase-space. For each
class, computational algorithms and validation exercises are briefly discussed.
