Hi Chao,

In real neurons, the refractory period arises from a combination of biophysical mechanisms. After firing an action potential, the cell needs to recover before it can fire another one. In simplified neuron models, such as most integrate-and-fire models, which do not include these recovery mechanisms, one usually adds an explicit refractory period to capture the effect of the biophysical recovery mechanisms in a mathematically or computationally simple way.

But if a neuron model includes (slow) recovery variables that will prevent it from spiking for some period after firing a spike, adding an explicit refractory period may not be required. Izhikevich decided that this was the case for his model, and thus there is no explicit refractory period that could be set as a parameter. The neuron model has its refractoriness simply "built in", with details depending on the parameters.

Best regards,

Hans Ekkehard