Those pointy corners rather trochoidialize the "typical lissajous". Its apparently a data-reduction modeling artifact.
Coherent periodic series do appear in "lucky" bursts in stochastic sequences. These can be hard to rule out. In fact, many physicists think our universe is a very lucky accident. Transient deterministic resonances also occur locally in chaos.
The ultimate test of geophysical conjecture is to predict the future. Peak Oil miscalculations offer a cautionary case from the Geoenergymath case-base (the effective limit to Oil Extraction based on fracking and tar-sands is the collapse of civilization, not depletion). To falsify [Mann et al, 2020], nothing better than a correct and repeatable multidecadal forecast.
Slide-1 stratigraphy on the page-link below seems to record decadal-multidecadal climate oscillations, never mind if they do not happen to match any specific claim made from modern observations.
Geoharmonics relentlessly vary with tectonic shifts on the geologic-timescale, and surely for many causes on the (multi) decadal scale.