It's way beyond a three body problem though, so it's chaotic even if it's recurrent... even trying to retrodict precise correlations in celestial events 10k years ago is difficult, doing this would be way harder. The only thing I can think of on that scale that's somewhat predictable within meaningful margins is Milankovich cycles. Cool paper though. Thanks for sharing.

(And to note: I can't edit my reply now but I read 'there' as 'these'. Obviously there are other (somewhat) cyclic natural catastrophes especially on shorter timescales.)

Sounds a little like Nemesis [1].

The Wikipedia article mentions 26 million year intervals. So we're probably good for another 10 million?

[1] https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star)

Everyone once in a while the roulette ball lands on green and I get a big payout. That's not a cyclical event.