Excitability inflection for exit problem in Class 1 excitable systems

Abstract

The path from resting to spiking threshold can generate a typical action potential in neurons. For excitable systems with ubiquitous noise, this process can be investigated in the framework of large deviation theory. In this paper, a special position (named as excitability inflection point) of the exit process in the canonical Class 1 excitable system is identified, which is both the extremal position of the dispersion and the momentum. The role of this point is examined by adding a Gaussian white noise and a pulse with a special position into the deterministic system. Surprisingly, by calculating the firing rate, its extremal position can be made closer to the theoretical excitability inflection point with vanishing pulse instead of vanishing noise. The influences of finite noise and pulse are investigated in detail by fixing one of them and changing the other. They showed distinct impacts on the real extremal positions of the firing rate. Finally, some open problems are given.