Overview of models of cellular excitability and future perspectives

 The main properties of the membrane dynamics of many excitable cell can  be modeled using a 2-dimensional model. This document contains a quick review of  relevant literature and an overview of important   characteristics of existing and well established models of transmembrane potential. Special attention is paid to a 2-dimensional reduction of the Hodgkin and Huxley model and the properties that  the reduction retains from the original model.The  Fitz-Hugh model is briefly reviewed after that,  followed by a brief account of modern contributions to the study of cellular excitability using dynamical  systems theory are mentioned. The basic steps  involved in constructing a unifying core model of excitability are outlined. The generic model can be used to establish explicit relationships between the bifurcation structures in low-dimensional models of   excitable cells and their electrophysiological profiles.