A discrete sequential tunneling model is used for studying the influence of the doping density on the dynamical behaviors in weakly coupled GaAs/AlAs superlattices.Driven by the DC bias,the system exhibits selfsustained current oscillations induced by the period motion of the unstable electric field domain,and an electrical hysteresis in the loop of current density voltage curve is deduced.It is found that the hysteresis range strongly depends on the doping density,and the width of the hysteresis loop increases with increasing the doping density. By adding an external driving ac voltage,more complicated nonlinear behaviors are observed including quasi- periodicity,period-3,and the route of an inverse period-doubling to chaos when the driving frequency changes. A discrete sequential tunneling model is used for studying the influence of the doping density on the dynamical behaviors in weakly coupled GaAs / AlAs superlattices. Driven by the DC bias, the system exhibits self -usted current oscillations induced by the period motion of the unstable electric field domain , and an electrical hysteresis in the loop of current density voltage curve is deduced. It is found that the hysteresis range strongly strongly on the doping density, and the width of the hysteresis loop increases with increasing the doping density. voltage, more complicated nonlinear behaviors are observed including quasi- periodicity, period-3, and the route of an inverse period-doubling to chaos when the driving frequency changes.