I'm not sure exactly what you mean, but with a constant voltage input the current settles quickly and then stays there.
That is, there doesn't seem to be any sort of long term variations, just the short term effects of bulb heating/cooling time and positive tempco, resulting from a significant variation in any of voltage, load, or current capacity.
As I mentioned it's not so good in a dynamic situation. So for example, from cold, the sudden application of voltage causes a heavy inrush current that then subsides to a constant steady current within a a couple of seconds.
But if the power source has current limiting, there is a strong possibility of wild oscillations, and I've had that happen once. It usually doesn't, as I'm generally winding up the input voltage relatively slowly via a variac, which avoids such violent current surges.