Singularity detection method of chaotic time series using wavelet multi-resolution analysis

In this paper, wavelet multi-resolution analysis (WMRA) is applied to detect singularity in chaotic time series. Based on the analysis of the relationship among wavelet multi-resolution, Lipschitz exponent and signal singularity, we select Daubechies wavelet to decompose the chaotic signal in different scales. After reconstructing those signals decomposed, some of which contain singular information, the position of singularity in signals can be exactly found out. Furthermore, because of the case that the existence of noise in real chaotic system, we test the anti-interference of WMRA with white noise. The research conclusions show that WMRA not only has a strong ability for detecting singularity of chaotic time series signal, but also has a good effect on anti-interference.