Markov chain model approximating the Hodgkin-Huxley neuron

Abstract

The Hodgkin-Huxley (HH) model well reconstructs a neuronal membrane potential. However, the HH equations, which are nonlinear ordinary differential equations with four variables, are not appropriate to simulate a large network because of the high complexity. In addition to the dynamical complexity, stochastic factors such as synaptic transmissions should be considered in a model neuron. In this paper, we propose the Markov chain model that statistically approximates firing patterns of the HH model.