Bistability Resulting from Rebound Firing

Abstract

We have seen that some model neurons have continuous, single-valued f-I curves. With the exception of the LIF neuron, all of these model neurons transition from rest to firing via a SNIC. Other model neurons have discontinuous f-I curves with an interval of bistability, in which both rest and periodic firing are possible. The examples we have seen transition from rest to firing either via a subcritical Hopf bifurcation, or via a saddle-node bifurcation off an invariant cycle. The distinction between continuous and discontinuous f-I curves closely resembles the distinction between “class 1” and “class 2” neurons made by Hodgkin in 1948 [75].