"Mine was doing that at well. It was the water in the tank filling up too much and running into the overflow drain. I was able to adjust the bulb-float and it hasn't done it since."
That should make the water run constantly, not switch on and off, unless your float is balanced just so that it doesn't quite cut off the supply when the water tops off. Since this is a new problem with a decade-old toilet, I'd suspect a leak instead of a bad adjustment.