We propose a two-dimensional piecewise linear spiking neuron model that combines the dynamical property of Hodgkin-Huxley neuron model and the analytical property of integrate-and-fire neuron model.We show that this framework allows a qualitative description of excitable systems through bifurcation theory but also a quantitative analysis of neuronal behavior through an explicit analytical representation of the state variables.A detailed analytical study of the model is presented.The model gives rise to new neuro-computational properties not present in one-dimensional integrate-and-fire neuron models.In experiments

using this model we simulated the spiking and bursting behavior of known types of cortical neurons.