Methods of random Melnikov process function are introduced to analyze the equation and the differential trajectory,the influence of non-Gaussian color noise on Duffing oscillator chaotic motion behavior is also studied,a new chaotic method for the sine wave parameter estimation in non-Gaussian color noise environment is given.

Duffing oscillators’ phase transformation from chaos to intermittent chaos is sensitive to the signals, whose frequency difference is little different from the reference signal, while it has immune to white noise and the signals, whose frequency is quite different from the reference signal.

This article,through studying bifurcation and singularity of Duffing equation,by making use of the characteristics that Duffing oscillators produce spectrum approximates to white noise after enough bifurcation under perturbation of weak sinusoidal signal,analyzes bifurcation equation of Duffing oscillators and spectrum features.

Study on reliability of chaotic oscillator in weak signal detection;

The Principle of Detecting Faint Characteristic Signal Based onChaotic Oscillator and its Application;

On weak signal detection in ship′s shaft-rate electromagnetic field based on chaotic oscillator

So chaos oscillator algorithm could be utilized to acquire degraded GPS signal.

The interaction in two dimensional weakly coupled chaotic oscillators;

On the basis of the characteristics of the Duffing equation s solutions, the chaotic oscillators are designed.

It is a find that chaotic oscillators is sensitive to faint periodic small signal by introduction about chaotic Duffing equation and detection of theory, and it can detect the faint periodic small signal in strong noise background.