  The present study investigates the spatio-temporal variability in the
dynamics of self-sustained supersonic reaction waves propagating through an
excitable medium. The model is an extension of Fickett's detonation model with
a state dependent energy addition term. Stable and pulsating supersonic waves
are predicted. With increasing sensitivity of the reaction rate, the reaction
wave transits from steady propagation to stable limit cycles and eventually to
chaos through the classical Feigenbaum route. The physical pulsation mechanism
is explained by the coherence between internal wave motion and energy release.
The results obtained clarify the physical origin of detonation wave instability
in chemical detonations previously observed experimentally.
