Phase Plane Analysis of Firing Patterns in the Adaptive Exponential Integrate-and-Fire Model

TL;DR

This paper uses phase plane analysis to systematically investigate and explain the diverse firing patterns of the Adaptive Exponential Integrate-and-Fire neuron model, enhancing understanding of neuronal dynamics.

Contribution

It introduces a phase plane analysis approach to elucidate the mechanisms behind various firing patterns in the AdEx model under different conditions.

Findings

The AdEx model can simulate six distinct firing patterns.

Phase plane analysis reveals the dynamic mechanisms of these patterns.

Results support applications in neuromorphic computing and brain-computer interfaces.

Abstract

The Adaptive Exponential Integrate-and-Fire (AdEx) model is a simplified framework that effectively characterizes neuronal electrical activity. The aim of this paper is to employ phase plane analysis to systematically investigate diverse firing patterns generated by the AdEx model under varying parametric conditions. We first introduce the fundamental equations and parameter configurations of the AdEx model to numerically simulate the six representative firing patterns in the AdEx model. And then we use phase plane analysis to explore the dynamic mechanism of these firing patterns under different input currents and parametric conditions. Our findings demonstrate that the AdEx model can simulate multiple firing patterns, including Tonic Spiking, Adapting, Initial Bursting, Busting, Transient Spiking and Delayed Spiking firing patterns. These results not only advance the understanding of complex electrophysiological phenomena in neurons but also provide theoretical foundations for applications in many fields like neuromorphic computing and brain-computer interfaces.