all have approximately the same frequency. This contrasts with the saddle-node scenario.

We conclude with the two different bifurcation sets, Fig. 20, corresponding to distinct routes to sustained oscillations in this neuronal model. Panel (a) shows the saddle-node bifurcation, yielding the sudden onset of suprathreshold oscillations at I~4.5mA. Panel (b) depicts the Hopf bifurcation with the gradual onset of subthreshold oscillations at I~19mA, growing rapidly to suprathreshold with I^26 mA.

In the presence of discrete synaptic inputs, the saddle-node system will generate an all-or-nothing depolarization - or chain of depolarizations - if

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