As another user mentioned, oscillating loops can achieve these phenomenon and they're extremely abundant in biology. The circadian rhythm is an excellent example of this behavior.
It's interesting the article says: ... even if there are no exogenous cues present, periodical patterns are still shown (1) indicating that these rhythms result from an internal time-keeping system. ... For humans, the most prominent circadian rhythm is the 24 h rhythm in the sleep-wake cycle.
I thought it's a well-studied fact that humans settle on a 30 hours sleep-wake cycle in constant light conditions?
Nathaniel Kleitman spent a month in a cave in 1938 studying sleep/wake cycles, and found that he could maintain a 28 hour cycle. He did this deliberately, however, and this does not reflect the circadian rhythm. Rather, this wake/sleep cycle depends on C (the circadian rhythm) and S, homeostatic effects that reflect the previous period of wakefullness. It's also entirely possible to sleep at any point in the circadian rhythm (as anyone who has napped will know), so the circadian rhythm can simply decouple in extreme wake/sleep cycles (e.g. 20h or 28h).
Also, even with the circadian rhythm not being preciesly 24 hours, it's still 24 hours with entertainment. That's the standard physiological condition; it really is a 24-hour cycle. Free-running is like removing a component of the clock, seeing that it doesn't keep 24-hour time, and calling it broken. That's not the case; entrainment is part of the process and how the body keeps coordinated with its environment.
I thought it's a well-studied fact that humans settle on a 30 hours sleep-wake cycle in constant light conditions?