electrical system failing

Hi, I have a 2004 Mazda Rx-8 with a JL Audio 1000/1 and a 12W7 that I've been running for almost 3 years.  Up until now, I've had no problems with my electrical system supporting this.  I am running an upgraded Optima Yellow top, but stock alternator.  Lately I've been having some problems.  My dash lights have been dimming significantly whenever the bass hits with the volume only moderately up, about half of where I usually listen to it.  I can usually blast it without much dimming.  Also, my LM-1, which is an Air/Fuel analyzer keeps giving a low battery signal and reboots.  My car also drives funny, kind of jerky, when I crank up the volume. 

So obviously something is failing, but I don't know how to tell if its my battery or alternator.  I measured my alternator voltage the other day.  With the car idling its around 13.7v.  With all accessories on its around 13.5v.  Seems a little low, but is this low enough to indicate a bad alternator?

Thanks,

My suggestion would be to measure voltages to verify where the problem is.. it could be something as simple as a bad connection. Check alternator output while under load, check to make sure the battery is still good, measure voltage drops and see what you find.

Jim