The structure, geometry, and dynamics of high-dimensional, complex systems is usually hidden under a profusion of numerical data. We show how to analyze signals from such systems using time-frequency analysis. Our method takes snapshots of the system in terms of its instantaneous frequencies through wavelet transforms, and can characterize key dynamical properties like the extent of chaos, resonance transitions and trappings. The wavelet method can follow the rapid variations of the instantaneous frequencies since it adapts the size of its window to the frequency, thereby yielding better frequency resolution than windowed Fourier methods. i
Reference: "Time-Frequency Analysis of Chaotic Systems", C. Chandre, S.
Wiggins and T. Uzer, Physica D Vol.181, pages 171-196 (2003).
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