The dynamics of stimulated Brillouin scattering in a finite-length, ho
mogeneous medium with the effects of temporal resonance detuning but n
o external feedback is examined numerically. The inclusion of resonanc
e detuning leads to nonstationary behavior of the wave amplitudes incl
uding periodicity, quasiperiodicity, and chaos. The results may have a
pplications to experiments with optical fibers and laser plasmas.