Resonate-and-fire neurons

We suggest a simple spiking model-resonate-and-fire neuron, which is similar to the integrate-and-fire neuron except that the state variable is complex. The model provides geometric illustrations to many interesting phenomena occurring in biological neurons having subthreshold damped oscillations of membrane potential. For example, such neurons prefer a certain resonant frequency of the input that is nearly equal to their eigenfrequency, they can be excited or inhibited by a doublet (two pulses) depending on its interspike interval, and they can fire in response to an inhibitory input. All these properties could be observed in Hodgkin-Huxley-type models. We use the resonate-and-fire model to illustrate possible sensitivity of biological neurons to the fine temporal structure of the input spike train. Being an analogue of the integrate-and-fire model, the resonate-and-fire model is computationally efficient and suitable for simulations of large networks of spiking neurons.