Abstract: In order to solve the problem of co-frequency weak signals quantitative detection with the double-well Duffing-van der Pol oscillator, it is found that the Poincare section can clearly distinguish the different states of the system. The detection statistics based on the Poincare section is constructed, and based on that, an effective method of signal detection is designed. Firstly, the Poincare section is numerical calculated, and the bifurcation diagram about the driving signal amplitude is obtained. Then, the detection statistics are constructed by calculating the variance of the amplitude distribution points in different states. Distribution intervals of detection statistics in different states are different, thus the signal can be judged according to the interval in which the statistical value falls. Through the simulation experiments, the critical statistics and detection intervals of the detection statistics under different angular frequencies are given, and the feasibility of this detection method is proved by comparing with the phase plane detection results. The results provide references for quantitative detection of weak signals.

Key words: weak signal, signal detection, double-well Duffing-van der Pol oscillator, Poincare section, detection statistic