Watching a few of the Steven Strogatz lectures on Nonlinear Dynamics and Chaos (at 1.75X speed) and he is recommending graphical representations to understand the patterns.

The practical problem with phase-space plots : The first two are clearly similar, but the 3rd is a wave composition that throws an obvious scaling pattern for a loop

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The LTE modulation fitting I am doing is essentially working backwards from the latter to the former, so there is quite a bit of cycle mixing that get's in the way. What I may try is phase-space plots on shorter intervals, which I can then display similar to a wavelet scalogram -- perhaps extending the plot into a depth dimension.