By numerical simulations we find that the Duffing state transition from big-cycle motion to chaotic motion is more suited to weak signal detection. Based on this, in this paper, we propose a new weak periodic signal detection method from the angle of theoretical analysis. The principle of the proposed method is introduced and its feasibility is analyzed. Then, the proposed method and the traditional method are compared and analyzed both in transition zone effect and detection probability, and then a contrast simulation is carried out. The analysis and simulation results both indicate, the Duffing oscillator state transition from big-cycle motion to chaotic motion is affected less by transition zone under the same condition, based on which the proposed detection method possesses better detection capability. The simulation data also show that weak signal detection with Duffing oscillator must be based on unilateral state transition. The frequency difference detection based on intermittent chaos is suited only for the case where the signal-to-noise ratio of the detected signal is relatively high.