If you use a battery-powered bike light that has a pulse capacity, you've probably noticed that as the battery starts to wear down, the frequency of pulses in the light reduces, until finally, when the light is very faint, the frequency of pulsing is incredibly low. In my non-timed estimation, I don't think the duty cycle of the light changes, that is, the ratio of time spent on versus time spent off stays the same. However, the duration of each of those times increases.

Why does this occur? (I would probably expect that a system as simple as this could be modeled effectively by an ODE of some kind, but I can't see why the frequency term in the solution to that ODE would be affected by the voltage available). I could probably see why it would be affected by the capacitance or the resistance of the circuit, but I'm not sure those would necessarily be affected by battery drainage.