▎ 摘　　要

Controlling dynamic behaviors, such as instability and chaos, in various systems has been a central matter of nonlinear physics in recent years. Here we employ an effective density- matrix method for the study of laser beam propagation through an optical ring cavity containing Landau-quantized graphene nanostructures. By taking into account the linear and nonlinear phase shifts, we detailedly investigate and characterize the nonlinear dynamic behaviors of the transmission field and the results show that the system exhibits dynamic instability. The start and termination, as well as the periodicity of this dynamic oscillations inside the optical cavity can be manipulated by the experimentally achievable parameters, such as the laser intensity and frequency detuning. Such dynamic responses are attributed to the competition between optical saturation of the incident field and population oscillations induced by the control field in graphene system.