Biomedical Engineering Reference
In-Depth Information
A
B
Excitation
Inhibition
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
0.5
1
1.5
2
0
0.5
1
1.5
2
Firing rate n (Hz)
Firing rate n (Hz)
Figure 15.4
Self-consistent solution of Equation (15.80) and its stability properties. The output
firing rate f
(
m
V
(
n
)
,
s
V
)
is plotted versus nin two situations.
(A)
Excitatory network
0mV,
J
4mV,
J
with m
ext
V
5mV.
(B)
Inhibitory network with m
ext
V
=
=
0
.
=
20
.
=
−
0
.
5
mV. Other parameters are:
C
=
1000, t
m
=
t
syn
=
20 ms (
C
m
=
0
.
5nF,
g
L
=
25 nS),
t
re f
=
5 mV. For both types of networks,
there is a self-consistent solution around 1Hz. In the excitatory network, this self-
consistent solution is highly unstable, because the slope of
2ms,
V
th
=
−
50 mV,
V
r
=
−
60 mV, s
V
=
vs. n is
much larger than one; in the inhibitory network, the self-consistent solution is highly
stable because of the large negative slope. In a balanced network where inhibition
strongly dominates the recurrent circuit, the slope becomes infinite negative. Note
that in the excitatory network, there are two other solutions: one at zero rate, and one
close to saturation rates (about 500 Hz).
f
(
m
V
(
n
)
,
s
V
)
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