  It has long been a standard practice to neglect diffusive effects in
stability analyses of detonation waves. Here, with the principal aim of
quantifying the impact of these oft-neglected effects on the stability
characteristics of such waves, we use numerical Evans-function techniques to
study the (spectral) stability of viscous strong detonation waves---particular
traveling-wave solutions of the Navier-Stokes equations modeling a mixture of
reacting gases. Remarkably, our results show a surprising synergy between the
high-activation-energy limit typically studied in stability analyses of
detonation waves and the presence of small but nonzero diffusive effects. While
our calculations do show a modest delay in the onset of instability in
agreement with recently reported calculations by direct numerical simulation of
the physical equations, our approach, based on the Evans function, also
provides additional spectral information. In particular, for each of the
families of detonation waves in our computational domain, we find a completely
unexpected kind of hysteresis in the limit of increasing activation energy;
that is, our calculations suggest that, whenever diffusive effects are present,
there is a return to stability as unstable eigenvalues return to the stable
complex half plane.
