i present an introduction into the mechanisms of generation of spikes and bursts in neurons and in hodgkin-huxley-type neuronal models. then i present a deterministic model that reproduces spiking and bursting behavior of known types of cortical neurons. the model combines the biologically plausibility of hodgkin-huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop pc. \vskip .1in \noindent matlab and c++ code, as well as pdf file of the paper are available at http://www.nsi.edu/users/izhikevich/publications/spikes.htm