Yes. Yet as far as I can tell there is no real consensus for ENSO. The split is between stochastic models and chaotic models and both can only give a statistical agreement. The non-chaotic deterministic model is the odd-man out because no one is looking at that approach. Somehow it was rejected long ago, even though the repeat cycle for a full lunisolar forcing is 372 years! With that long a period, hard to tell the difference between a cyclic behavior and one that is chaotic or random.

IMO, a deterministic model was dismissed too soon and it became conventional wisdom not to look at it again.

Interesting that in regard to the 372 year repeat period, which is the same as the recurrence of eclipses on the same day of the tropical year:
>Stockwell, John N. "On the law of recurrence of eclipses on the same day of the tropical year." The Astronomical Journal 15 (1895): 73-75.

Sure enough, the model calculation I use follows this cycle fairly closely. Consider that the graph below is a combination of the 3 lunar sine waves plotted on precisely 1 year intervals (which provides the same day of the tropical year)


You can detect the general 372 year repeat period from comparing the two blue arrow intervals, and there is another repeat period of 1230 years which you can see by shifting and aligning two intervals. Both of these repeat periods are subtle and it's not surprising that it's not picked up in any natural phenomena apart from something as striking as a eclipse, where the 372 year cycle has been long known.

When the \\(1/R^3\\) forcing and the ephemeris corrections to the sine waves is invoked, we can compare to the data and how it appears when it is shifted by 372 years.


It's not perfect because the 372 year period is not perfect, but it's enough to understand how the repeat period is preserved even after the perfect sine waves are individually distorted by the same base 4 frequencies.