Here in East Texas, the rut will usually start at just about the same time each year, within about a week or so, year to year. Photoperiods govern this pretty well.
So, why is the rut strong one year and not the next?
I think the " strength" of the rut is just what we see.
The deer are going to breed, so its going to get done!
I think that moon phase, weather, hunting pressure and yes, food play a part in how much of the rut that we see. When the conditions are right, (for hunters) we see more rut activity, such as scrapes and chasing, and we say that the rut is strong.
The same conditions that make deer move more during the rut, are conditions that will make them move more to feed in daylight hours. I think that bucks that are moving more to feed, due to lack of abundant mast, will just naturally cover more ground and naturally leave more " calling cards" as he goes.
So I think that the only time that food would have any REAL effect on the rut would be if there is not enough food and the deer are in poor health!