This Demonstration simulates the two-dimensional persistent sodium plus potassium (

) neuron model described in [1].

where

is the capacitance density (for the squid axon,

, so

is fixed and set to one);

is the voltage across a cell membrane in mV;

is the total current density flowing across a patch of the cell membrane in

;

,

,

are the equilibrium potentials (reverse potentials) in mV;

,

,

are conductance densities in

;

and

are the activation variables (probabilities of activation gates to be open) and when with the subscript

, they are voltage-sensitive steady-state activation functions; and

is the time constant. Note that

stands for leak (ohmic leak current density is given by

and it is mostly carried by

ions);

and

are sodium and potassium ions, respectively. Finally, the Boltzmann functions

and

each have two parameters:

and

, where

satisfies

and similarly for sodium. The

,

are slope factors; that is, they adjust the slope of the Boltzmann functions at

(smaller values of

result in a steeper Boltzmann function).

We plot four graphs. The main graph is the phase plane of the potassium conductance versus membrane voltage with the vector field (black), nullclines (orange and green), and voltage trajectory (red) superimposed. We also plot the membrane voltage versus time, sodium (

) and potassium (

) conductances versus time, and membrane currents versus time. Blue corresponds to sodium and green to potassium; nullcline is green as well.