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A Balance Equation Determines a Switch in Neuronal Excitability
Figure 6
Variations of the potassium reversal potential 
induce excitability switches in the Hodgkin-Huxley model.
A. Bifurcation diagram of the HH model with 
as the bifurcation parameter. TC denotes a transcritical bifurcation, SN a saddle-node bifurcation, HB a Hopf bifurcation. Branches of stable fixed points are represented as solid curves, whereas branches of saddle points and unstable points as dashed curves. B. Electrophysiological responses of the model for three different values of 
, corresponding to three different excitability types (restorative, mixed, and regenerative, from left to right). C. Bifurcation diagrams with the applied current as the bifurcation parameter for the same three values of 
as in B. Black (resp. blue) full curves represent branches of stable steady-states (resp. limit cycles), black dashed curves branches of saddle and unstable steady-states. Branches of unstable limit cycle are drawn as dashed blue curves. HB denotes a Hopf bifurcation, SN a saddle-node bifurcation, and SH a saddle-homoclinic bifurcation. D. Phase portraits of reduced HH model proposed by Rinzel in [10] for the same three values of 
as in B,C. Blue full curves denote the 
-nullclines and black full curves the 
-nullclines, where 
denotes the slow variable of the reduced model. Filled circles denote stable steady-states, crosses saddle points, and circles unstable steady-states.
doi: https://doi.org/10.1371/journal.pcbi.1003040.g006