Numerical simulation results are presented for a drift-diffusion rate equation model which describes electronic transport due to sequential tunneling between adjacent quantum wells in weakly coupled semiconductor superlattices(SLs). The electron dynamics is dependent on the external magnetic field perpendicular to the electron motion direction, and a detailed explanation is given. Using different parameters, the system shows different dynamic behaviors, and three distinct phenomena are observed and controlled by increasing magnetic field.(i) For a lower doping density, the system state transfers from stable state to oscillationary state.(ii) An opposite result is obtained to that in the case(i) for an intermediate value of the doping density, and the state changes from oscillationary to stationary.(iii) The state varies between oscillationary and stationary when doping density is large. Then, a detailed theoretical analysis is given to explain these surprise phenomena. The distribution of the electric-field domain along the SLs is plotted. We find the structure of the domain is almost uniform for a lower doping density, and no domain occurs in the SLs. By adding an external ac signal, complex nonlinear behaviors are observed from the Poincare′ map and the corresponding phase diagrams when the driving frequency changes. Numerical simulation results are presented for a drift-diffusion rate equation model which describes electronic transport due to sequential tunneling between adjacent quantum wells in weakly coupled semiconductor superlattices (SLs). The electron dynamics is dependent on the external magnetic field perpendicular to the electron motion direction , and a detailed explanation is given. Using different parameters, the system shows different dynamic behaviors, and three distinct phenomena are observed and controlled by increasing magnetic field. (i) For a lower doping density, the system state transfers from stable state to oscillation (ii) An opposite result is obtained to that in the case (i) for an intermediate value of the doping density, and the state changes from oscillation to stationary. (iii) The state varies between oscillation and stationary when doping density is large. Then, a detailed theoretical analysis is given to explain these surprise phenomena. The distribution of the electric-field domain along the SLs is plotted. We find the structure of the domain is almost uniform for a lower doping density, and no domain occurs in the SLs. By adding an external ac signal, complex nonlinear behaviors are observed from the Poincare ’map and the corresponding phase diagrams when the driving frequency changes.