The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscillator system to detect weak signals. The restoring force term of the system affects the weak-signal detection ability of the system directly, the quantitative relationship between the coefficients of the linear and nonlinear items of the restoring force of the Duffing oscillator system and the SNR in the detection of weak signals is obtained through a large number of simulation experiments, then a new restoring force function with better detection results is established.
Taking the advantage of CVS (Chaotic Vibrator System) sensitivity of large-scale periodic phase-state response to quasi-periodic or periodic signals,a series of numerical experiments were made to understand the ability of CVS to detect weak effective seismic signals in the common-shot seismic record distorted by strong stochastic noise. The re-sults demonstrate that the large-scale periodic phase-states of CVS are correlated with the signal composition of the quasi-periodic wavelet sequence constructing from horizontal moveout of seismic events,noise strength and the noise distortion de-gree to signal. For the same kind of events,the higher the noise distortion degree is,the lower the detectable SNR can be reached by CVS. For seismic data with the same noise distortion degree,the closer the scanning seismic velocity (the trial moveout ve-locity) approaches to the accurate velocity,the higher the detectable SNR can be reached by CVS. More-over,the truncating scanning velocities form an asymmetric belt,which indirectly makes CVS achieve a large-scale periodic phase-state and then the ratio of wavelet distortion coefficients in events can be a biggish variable scope.
