On the Capabilities and Computational Costs of Neuron Models

We review the Hodgkin-Huxley, Izhikevich, and leaky integrate-and-fire neuron models in regular spiking modes solved with the forward Euler, fourth-order Runge-Kutta, and exponential Euler methods and determine the necessary time steps and corresponding computational costs required to make the solutions accurate. We conclude that the leaky integrate-and-fire needs the least number of computations, and that the Hodgkin-Huxley and Izhikevich models are comparable in computational cost.