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I have some experience in non-linear system identification (from an experimental point of view) using higher oder spectral analysis. I see this is the most popular way of identifying non-linearities from a system using the normalised bispectrum (bicoherence) both ordinary fourier and wavelet based bispectra.

I have 3 questions:

  1. Is there a Mellin-based normalised bispectrum that has been defined and normalised appropiately for a similar application?

  2. Is there a method based on tracking the time evolution of the curvature of said system's phase-plane portrait?

  3. Vaguely related to 2 above, Is it possible to obtain enough information about the time evolution of a system say for example a deformable body submerged in a vector field by observing the curvature of the surface (Particularly, Components of the Riemann-Chrisoffel curvature tensor?)

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