Information Technology Reference
In-Depth Information
a
b
1
0.4
0.3
0.5
0.2
0
0.1
−0.5
0
5
10
15
20
25
30
35
40
0
time (sec)
0.4
−0.1
0.2
−0.2
0
−0.3
−0.2
−0.4
−0.4
0
5
10
15
20
25
30
35
40
−0.4
−0.2
0
0.2
0.4
0.6
time (sec)
x
1
Fig. 1.9
(
a
) State variables of the FitzHugh-Nagumo neuron exhibiting sustained oscillations, (
b
)
limit cycles in the phase diagram of the FitzHugh-Nagumo neuron
examines the variation of the membrane's potential in a neuron as a function of the
conductances of the associated ionic channels and contains also a second differential
equation which expresses the probability an ionic channel to be open. The model's
equations are:
C
M
d
dt
D I
app
g
L
.V E
L
/ g
k
.V E
k
/ g
Ca
m
1
.V/.V E
Ca
/
D I
app
I
ion
.V;n/
(1.57)
d
dt
D .
1
.V/ /=
.V/
where
2
h
1 C tanh
V
V
1
V
2
i
1
m
1
.V/ D
1
cosh..V V
1
/=2V
4
/
.V/ D
(1.58)
2
h
1 C tanh
V
V
3
V
4
i
1
m
1
.V/ D
Here, parameters V
i
;iD 1; ;4are chosen to fit data obtained from an identi-
fication procedure. Although it is more simple comparing to the Hodgkin-Huxley
model (the latter expressed either in a PDE or set of ODEs form), the Morris-Lecar
model captures efficiently several properties of the biological neurons.
