I know the question is a little vague, but I would like to know if someone can direct me to what kind of oscillator (if exist), that can follow the next behavior.

*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.

Thanks!