The role of the dendritic tree and the way it functions within a neuron has been of interest to neurologists for over a century. As investigative techniques have become more sophisticated and thus revealing, our perception of the dendrites as being purely an information gathering component has changed to one where the dendritic tree may be viewed as a highly complex, nonlinear information processor. In spite of this most mathematical studies of the dynamical behaviour of neural populations have neglected the influence of the dendritic tree. The aim of this thesis is to address this imbalance.