greetings back!
yes, there is a branch of solar physics which specifically studies the solar cycle and its cause. generally it is not focused on the production of a single sunspot or another, but rather on the cause of the overall increase and decrease of magnetic activity on the 11 year activity cycle. In fact, every 11 years the overall direction of the magnetic field for the sun flips, so that in fact the real cycle is closer to 22 years long.
the mechanism which is believed to underlie the solar activity cycle is called the Solar Dynamo. You may be interested to read a little bit about how people who study the solar dynamo made predictions over the last few years about the start and the intensity of the next solar activity cycle. See http://www.swpc.noaa.gov/SolarCycle/, and another good site is http://solarscience.msfc.nasa.gov/predict.shtml
the bottom line is, though, is that while we think we understand the general principles behind the solar magnetic cycle ( it is caused by the interaction of the solar rotation as a function of depth combined with the interaction of the ionized plasma and the global magnetic field), most of the details we do not understand, so that we really are not yet able to reliably predict what will happen next with the solar cycle.