Study of chaotic dynamical systems via time-frequency analysis

Time-frequency representation is helpful in studying the frequency pattern of nonlinear dynamical systems. Specifically, the Wigner-Gabor-Qian (WGQ) spectrogram, a synthesis of the Wigner distribution and the Gabor expansion through time-frequency distribution series, is a very useful tool because it achieves a good solution in time-frequency representation as well as few cross-interferences. The fine structure of frequency patterns, such as sub-harmonics of chaotic dynamics, can be revealed by the WGQ spectrogram. Frequency patterns of chaos and noise are studied for system identification in empirical analysis. Time-frequency analysis provides important information for pattern recognition and system identification in analyzing empirical time series