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**Hodgkin-Huxley Nerve Model**

exd14

Variables and parameters:
*U* (*t*): membrane potential of a nerve cell
*V*_{1}, *V*_{2},*V*_{3}: artificial variables defining permeability of the membrane
*I*_{a}: applied current (
bifurcation parameter)

transfer rates:

Figure 1

(*U*,*V*_{1})-phase diagram of the Hodgkin-Huxley equation; two trajectories: *U*(0)=-5 and -6, with
*V*_{1}(0)=0.31,
*V*_{2}(0)=0.05,
*V*_{3}(0)=0.6 and *I*_{a}=0.

Figure 2

*U*(*t*) for
;
Hodgkin-Huxley equation; two trajectories: *U*(0)=-5 and -6, with
*V*_{1}(0)=0.31,
*V*_{2}(0)=0.05,
*V*_{3}(0)=0.6 and *I*_{a}=0.

Figure 3

(*U*,*V*_{1})-phase diagram of the Hodgkin-Huxley equation; trajectory approaching a limit cycle. *U*(0)=-5,
*V*_{1}(0)=0.31,
*V*_{2}(0)=0.05,
*V*_{3}(0)=0.6 and *I*_{a}=-10.

Figure 4

(*U*,*V*_{1})-phase diagram of the Hodgkin-Huxley equation; six trajectories *U*(0)=*U*_{0}, with
*V*_{1}(0)=0.31,
*V*_{2}(0)=0.05,
*V*_{3}(0)=0.6 and *I*_{a}=0;
*U*_{0}=-5.0/-5.2/-5.4/-5.6/-5.8/-6.0

Figure 5

*U*(*t*) for
;
membrane potential of the Hodgkin-Huxley equation; six trajectories *U*(0)=*U*_{0}, with
*V*_{1}(0)=0.31,
*V*_{2}(0)=0.05,
*V*_{3}(0)=0.6 and *I*_{a}=0;
*U*_{0}=-5.0/-5.2/-5.4/-5.6/-5.8/-6.0

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