中文摘要：

通过对杜芬（Duffing）方程的分岔与奇异性的研究，利用弱正弦信号扰动下杜芬振子经过足够多的分岔会产生近似白噪声的频谱特性，对杜芬振子的分岔方程和解态频谱进行分析，证明白噪声信号与混沌信号属于同一类信号，本文首次验证了确定系统混沌信号的频谱与噪声随机信号的相似性。

英文摘要：

This article, through studying bifurcation and singularity of Duffing equation, by making use of the characteristics that Duiffing 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. It proves that white noise signal and chaotic signal belong to the same type. It verifies the similarity of spectrum of chaotic signal in determination system and stochastic signal for the first time.