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. T...