The adaptive exponential integrate-and fire (aEIF) model is a spiking neuron model that was proposed by Brette and Gerstner in 2005. Since then it has been used in multiple empirical and modeling papers. For example, we have used it to describe the age-related changes in neural adaptation observed in human electroencephalographic recordings (journal webpage; pdf). Scholarpedia provides a good overview of the model and its relation to other neuron models. The aEIF model consists of two differential equations and by adjusting the parameters of the model, it is capable of describing known neuronal firing patterns. Three examples are displayed below:
In this example, a tonic bursting response patterns is elicited for a constant current input.
In this example, a hyper-polarizing current leads to rebound firing following inhibition.
In this example, a current step leads to subthreshold oscillations and resonance phenomena.