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The sensitivity of the system to parameters is equivalent to the sensitivity of the initial value. When we study the output transition process corresponding to different initial values, we find that there are three kinds of output transition process: chaotic-periodic transition process, periodic-chaotic-periodic transition process, periodic-chaotic transition process. A variable scale weak signal detection method is proposed to detect the same frequency weak signal. Analysis of output waveform characteristics of Duffing system, we give the quantitative relationship between the input signal to be measured and the output signal. Multi-form joint discriminant method for conventional Duffing chaotic systems can make the detection result easier to identify and more reliable, and reduce false alarm probability and false alarm probability.

Duffing chaotic systems are sensitive to certain signals and immune to noise, the properties of which demonstrate their potential application in weak signal detection. Determination of critical value for abrupt change of the Duffing system is important theory basis for Duffing oscillator system. A solving formula of the critical value of Duffing oscillator system is obtained by using harmonic balance analysis method. The simulation results show that the theoretical solution and numerical simulation are preferably coherence. Noise can cause the false alarm detection. Based on the sensitivity of damping ratio, the variable damping ratio Duffing oscillator detection method with variable amplitude coefficients is introduced to reduce the false alarm caused by noise. To overcome the shortcomings of the phase diagram discrimination method in quantitative analysis, a detection statistics identification method is proposed. The results of the experiment verify the feasibility and accuracy of the new approach.

A detection method based on variable damping ratio is proposed for the problem of Duffing chaotic oscillator system's false alarm detection generated by noise. The Duffing oscillator detection method has the ability of weak signal detection based on the sensitivity of driving force amplitude. But the noise can cause the false alarm detection. Based on the sensitivity of damping ratio, the Duffing oscillator detection method can detect different amplitude signals by adjusting damping ratio. Combining the advantages of the above two detection methods, the variable damping ratio Duffing oscillator detection method with variable amplitude coefficients (VDVA-Duffing) is introduced to reduce the false alarm caused by noise. To overcome the shortcomings of the phase diagram discrimination method in quantitative analysis, a Lyapunov exponent identification method with variable damping ratio is proposed. The results of the experiment verify the feasibility and accuracy of the new approach.