In this talk, we will discuss the influence of inhibition on an activity-based neural field model consisting of an excitatory population with a linear adaptation term that directly regulates the activity of the excitatory population. Such a model has been used to replicate cortical traveling wave data as observed in clinical recordings. We will establish conditions for the existence of traveling wave solutions with properties observed in in vivo data. We will also discuss some results concerning the linear stability of traveling wave solutions of this model via the construction of an Evans function.