  Direct observation of a Rotating Detonation Engine combustion chamber has
enabled the extraction of the kinematics of its detonation waves. These records
exhibit a rich set of instabilities and bifurcations arising from the
interaction of coherent wave fronts and global gain dynamics. We develop a
model of the observed dynamics by recasting the Majda detonation analog as an
autowave. The solution fronts become attractors of the engine; i.e.,
mode-locked rotating detonation waves. We find that detonative energy release
competes with dissipation and gain recovery to produce the observed dynamics
and a bifurcation structure common to driven-dissipative systems, such as
mode-locked lasers.
