  We show that transition to longitudinal instability of strong detonation
solutions of reactive compressible Navier--Stokes equations is generically
associated with Hopf bifurcation to nearby time-periodic "galloping", or
"pulsating", solutions, in agreement with physical and numerical observation.
In the process, we determine readily numerically verifiable stability and
bifurcation conditions in terms of an associated Evans function, and obtain the
first complete nonlinear stability result for strong detonations of the
reacting Navier--Stokes equations, in the limit as amplitude (hence also heat
release) goes to zero. The analysis is by pointwise semigroup techniques
introduced by the authors and collaborators in previous works.
