[GistNoesis]

If I understand the article correctly, it is a less strong constraint on the signal than being periodic, like an oscillator would be. The signal is only periodic for specific value of time, in between those value of time the signal is not periodic.

To give a music analogy, the constraint is like always play the same chord on the first beat of each measure. In between you are free to play whatever chords you like.

How does a physical system can acquire such property? I have no idea that's the mystery a physicist will have to explain.

[rfhjt]

Can it be just a sum of periodic signals? For example if one signal has a period of 7 and another of 11, the period of their sum is 7x11.

[GistNoesis]

No, that's something different, there is a definite state that is visited at a regular interval.

I get your idea of using various periods : If instead of a sum of periodic signals, you do something completely nonphysical like a product cos(x)cos(x/3)cos(x/5)cos(x/7)any_f(x) you can observe indeed that the zero crossings come back periodically. (Edit: something kind of an amplitude modulation may not be so nonphysical after all)