I manually create the gif to try to explain the problem.
It's a wave with a discrete number of maximum amplitudes. In the example there are four of those points on the red line.
What I have in mind is probably a chaotic oscillator that always cuts a line or plane (in the graph the Y axis) on the same points.
I have checked information about chaotic oscillators, and also some information about quasiperiodic motion, but I need some help on how to proceed or what to keep looking.
In the end, what I really want is a chaotic oscillator that cuts a line or plane, in only some discrete number of points. Is it possible?
Hope it makes sense.