@pannell regardless of what vehicle you have, you do want to make sure that your wiring is clean and tight on the terminals and the battery. You could go with a higher amperage alternator but that may not fix it completely due to the spikes in power demand. This will of course depend on your vehicle and which alternators are available. I'd suggest you add a capacitor to your vehicles sound system as well. The cap would smoothen out the power spikes. It should prevent those spikes that draws from your electrical system. Rule of thumb is 1 Farad per 1000W RMS
This site should help you how to conect the caps(s). Brax, Boss, Alumapro and Fosgate have a couple of decent size caps that are meant for this purpose.