Most units in deep learning are described by their output for a given input. An oscillator is better described by its orbit: the shape it settles into regardless of where it started.
ẋ = y
ẏ = μ (1 − x²) y − x
In the phase portrait above, every arrow points the way the system would move from that point, and the trajectories spiral into the same closed loop. That loop is the limit cycle.
The question
Could information be carried in the phase, frequency, or shape of an orbit rather than in a single activation? People have explored versions of this for decades. It is worth revisiting with modern training tools in mind.