With the development of chaos theory, Duffing oscillator has been extensively studied in many fields, especially in electronic signal processing. As a nonlinear oscillator, Duffing oscillator is more complicated in terms of equations or circuit analysis. In order to facilitate the analysis of its characteristics, the study analyzes the circuit from the perspective of vibrational science and energetics. The classic Holmes-Duffing model is first modified to make it more popular and concise, and then the model feasibility is confirmed by a series of rigorous derivations. According to experiments, the influence of driving force amplitude, frequency, and initial value on the system is finally explained by the basic theories of physics. Through this work, people can understand the mechanisms and characteristics of Duffing oscillator more intuitively and comprehensively. It provides a new idea for the study of Duffing oscillators and more.

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This paper studies the implementation of weak signal detection chaotic oscillators. Also, the detection model of the system is theoretically studied and analyzed. The main mechanism of the chaotic oscillator detecting the same frequency signal and the non-frequency signal located in the difference frequency range is expounded. The dissertation provides a reference for the realization of weak signal detection using chaotic oscillator.

Aiming at the blind angle in detecting weak signals of the same frequency by Duffing oscillator, a novel method of dephasing for the driving signals is proposed to eliminate the blind angle. According to the characteristic of weak signals, expression of blind angle is analyzed, and then the range of blind angle is found out, which corresponds to the amplitude of a new driven signal synthesized from the original driven signals and the unknown one. By making the original driven signal phase shift a degree of π, detection for the same frequency signal can be realized when the synthesized signal is located in the blind angle region, whose feasibility is proven by an experiment that it remains in chaotic status in the case of blind angle but becomes a great period status after the original driven signal's phase is dephased by π. To overcome the drawbacks of qualitative analysis and distinguish effectively different status in signal detection course, a detection statistics based on likelihood-Halmiton system is constructed. On the basis of it, a diagram of detection for any frequency signal is drawn. The key point is to make it as an unknown signal's frequency range where there are two adjacent frequency values whose corresponding detection statistics both located in the range of intermittent chaotic status, while one of them is just corresponding to the maximum value of the detection statistics. By simulations of different circumstances, detection statistics for numerical ranges of chaos, intermittent chaos, and great period is summarized. Furthermore, detection for any frequency signal may be realized by use of the numerical range. It is shown that the proposed method could not only provide quantitative judgment for the system status, but improve the signal detection performance. Also, it could be combined well with the traditional oscillator array method or adaptive step intermittent chaotic oscillator method, which further can improve some existing signal detection methods with Duffing oscillator.

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