Based on the mathematical description of current regulator, SPWM and PM motor, the mathematical model of a brushless DC motor system was proposed directly and transformed to a similar Lorenz system by applying the nonlinear affine transformation and the scaling transformation theory. The stability and attractor of the system were analyzed, and the relationship between the system operation condition and the direct current input was obtained. The stability of the three equilibrium points was analyzed by calculating the eigenvalues of the Jacobi matrix, which revealed that the Hopf bifurcation resulted in the strange attractor. Finally, numerical simulations were presented, and the results showed the validity of the theoretical analysis.