Research On The Influence Upon Roughness Of Duffing Oscillators Phase Trajectory's Edge By Noised Signal

With the development of the theory of Chaos, the superiority of utilizing Duffing chaotic oscillator to detect weak signal is more outstanding. The detection measure is based on the change of phase trajectory to judge the existence of the signal. But in actual detection process, noise is contained in signal, which is unavoidable, and the value of the noise from phase trajectory could not be obtained. SNR (signal noise ratio) is an important parameter in the procedure of signal detection, so we try our best to seek a way of determining the SNR from the phase trajectory.This paper studied the law between SNR and the roughness which was based on the influence between noised Duffing chaotic oscillator and large-scale period edge, then drew a conclusion that in the detection process the influence between noise and the roughness of large-scale period phase trajectory could be described in multiple harmonic function. So SNR wass determined through restructuring phase space for noised Duffing time series.This paper systematically introduced the basic concepts of chaotic dynamics, characteristics and Criteria. Based on the mathematical model of Duffing Oscillator, chaotic threshold of different nonlinear Duffing oscillator is elaborated in detail by the means of Melnikov. According to stochastic differential equation theory, the characteristical of 2 measures utilizing Duffing Oscillator to detect weak signal was analyzed, then the statistical characteristics of noise through chaos detection system was described quantitatively. The feasibility and the superiority of the chaotic detection were demonstrated.The influence law between SNR and phase trajectory edge was studied mainly because signal inevitably was affected by noise in actual detection process. Weak sinusoidal signal, weak square wave signal and weak cycle signal were set as research objects, and SNR was increased in the interval of 1dB. After 40 samples, one period was obtained, and then function was got by imitating. If the roughness of amplitude was known, multiple possible values were calculated. Then according toγvalue SNR interregional was drawn out, that is the only SNR. After reliable verification, relative error of this judgment did not exceed 1%.Finally in order to study the relationship between SNR of signal containing noise and trajectory average discrete distance (ADD), the method of phase space reconstruction was adopted for Duffing time series containing noise. One means of estimating value was probed through the data simulation. The simulation results showed that the relative error of the SNR is less than 1%, and this would cause positive significance to determine the value of the noise.