Professor Eric Shea-Brown has written up a nice website explaining what we're doing with the computational neuroscience modeling. It's currently on the Why Do Math website at this link: Brain Dynamics: The Mathematics of the Spike.
For my project, we're starting with a simpler model that is similar in behavior but quicker computationally and (somewhat) easier to analyze mathematically, known as the Izhikevich model(after its creator, Eugene Izhikevich). His website has some amazingly cool videos and a lot of papers on what he's been doing. His Website