Type III neurons, arguably the least studied class of neurons, have very distinct properties. In particular, neurons classified as Type III may exhibit transient spiking to current injection, but they will not fire continuously no matter how much excitatory current is applied. This property has been considered as advantageous in settings, such as processing of certain auditory stimuli, where each individual spike carries significant meaning or where processing of a rapid stream of stimuli occurs and requires avoidance of overlapping response windows. Rinzel and collaborators discuss a range of interesting input processing features that they describe as being associated with Type III neurons, including post-inhibitory facilitation (PIF), slope detection, phase locking, and coincidence detection. In this talk, I will present rigorous results on PIF and slope detection in a planar, hybrid neuronal model that combines continuous evolution of trajectories up to a spiking event defined by the finite-time blow-up of the voltage variable together with a discrete jump condition that resets positions of trajectories after spiking occurs.
427 Thackeray Hall