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. Author manuscript; available in PMC: 2009 May 1.
Published in final edited form as: Neural Comput. 2008 May;20(5):1239–1260. doi: 10.1162/neco.2007.05-07-536

Figure 4. Phase portraits of the Abbott-Kepler neuron model.

Figure 4

(a) The neuron fires repetitively to a mean current of 50 μA/cm2 when sodium conductance is high (GNa = 120 mS/cm2) such that the conductance values lie above the plane of Eq. (5) but (b) does not fire repetitively when the sodium conductance is low (GNa = 50 mS/cm2). The straight black line is the U nullcline corresponding to dU/dt = 0, where U is a general recovery variable, while the curved black line is the V nullcline, satisfying dV/dt = 0, where V is the membrane voltage. The gray lines are the trajectories of (V,U) in time, where the loops in (a) are the limit cycles of spikes. For a mean of 20 μA/cm2 and SD of 4 μA/cm2, spike initiation is dominated by (c) the internal dynamics when GNa is high but (d) when GNa is low, spikes are initiated by input variance. The fixed points in the two cases are (c) unstable, open circle, and (d) stable, closed circle, respectively. For (c) and (d), I = 20 μA/cm2. Other model parameters include: GK = 36 mS/cm2 and GLeak = 0.3 mS/cm2.