Return Map of a Periodically Driven Neuron

Abstract

A typical neuron receives input from more than 10,000 other neurons. These inputs each get processed differently, depending on the neuron's morphology, chemistry, etc. The neuron may fire, in turn stimulating other nerve cells. The structure of a nerve cell determines the rules that govern the system but not the neuronal response. Also, the type of input affects the firing decision. Hence, a neuron can be viewed as a dynamical system and may be studied as such. The Hodgkin-Huxley model describes neuronal dynamics but this model is very complex. Here, I will study some simpler models in an attempt to determine what makes a neuron fire. In particular, I will ask: What is the effect of "rhythmic" impulses on a neuron?