Threshold curve for the excitability of bidimensional spiking neurons

We shed light on the threshold for spike initiation in two-dimensional neuron models. A threshold criterion that depends on both the membrane voltage and the recovery variable is proposed. This approach provides a simple and unified framework that accounts for numerous voltage threshold properties including adaptation, variability, and time-dependent dynamics. In addition, neural features such as accommodation, inhibition-induced spike, and postinhibitory (-excitatory) facilitation are the direct consequences of the existence of a threshold curve. Implications for neural modeling are also discussed.