8 March 2002 Time-frequency representations applied to canonical Newtonian gradient forms: I
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Canonical polynomial forms taken from Thom's cuspoid family of catastrophes are studied as anharmonic oscillator potentials via time-frequency representations. Polynomial coefficients are control parameters, allowed to vary with time, inducing sudden changes in instantaneous equilibrium positions as well as characteristic oscillations about those equilibria that exhibit slowly varying spectra. Higher order potentials organize lower order potentials, which are contained in the higher order potentials, resulting in similar time-frequency signatures of the Newtonian dynamics ensuing as the potential changes with time.
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David H. Hughes, "Time-frequency representations applied to canonical Newtonian gradient forms: I", Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); doi: 10.1117/12.458749; https://doi.org/10.1117/12.458749

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