A discrete drift model of sequential resonant tunneling in weakly-coup
led doped or undoped GaAs/AlAs superlattices (SL) under d.c. or d.c. a.c. voltage bias and laser illumination is analyzed. In agreement wi
th experiments our model shows an oscillatory I-V diagram for large en
ough values of the doping and/or laser illumination, multistability an
d hysteresis between stationary solutions and self-sustained time depe
ndent oscillations of the current. Numerical and asymptotic analyses o
f the model show that these current oscillations are due to the format
ion, motion, annihilation and regeneration of negatively charged domai
n walls on the SL. For appropriate d.c. + a.c. voltage bias, chaotic c
urrent oscillations with loss of spatial coherence of the electric fie
ld will appear due to random nucleation of domains in the SL.