Dynamics of synaptically-interacting integrate-and-fire neurons

Travelling waves of activity have been experimentally observed in many neural systems. The functional significance of such travelling waves is not always clear. Elucidating the mechanisms of wave initiation, propagation and bifurcation may therefore have a role to play in ascertaining the function of such waves. Previous treatments of travelling waves of neural activity have focussed on the mathematical analysis of travelling pulses and numerical studies of travelling waves. it is the aim of this thesis to provide insight into the propagation and bifurcation of travelling waveforms in biologically realistic systems. There is a great deal of experimental evidence which suggests that the response of a neuron is strongly dependent upon its previous activity. A simple model of this synaptic adaptation is incorporated into an existing theory of strongly coupled discrete integrate-and-fire (IF) networks. Stability boundaries for synchronous firing shift in parameter space according to the level of adaptation, but the qualitative nature of solutions is unaffected. The level of synaptic adaptation is found to cause a switch between bursting states and those which display temporal coherence. [Continues.]