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where
g
FP
represents the maximal amplitude of the inhibitory coupling and
V
FP
=
V
FF
is the corresponding reversal potential. The time evolution of
s
FP,k
(
t
) is determined by
ds
FP,k
(
t
)
dt
=
T
(
V
k
)(1
s
FP,k
)
s
FP,k
/τ
i
(17)
−
−
where
T
(
V
k
)=2(1+
tanh
(
V
k
/
4) and
τ
i
=10
ms
is the decay time constant.
The electrical coupling among FS interneurons is all-to-all and the correspond-
ing current on the
j
th
cell is defined as
−
1
k
=
j
1
N
FS
−
J
FF,j
=
g
el
(
V
j
−
V
k
)
(18)
where
g
el
is the coupling amplitude. The parameters values
g
i
,g
e
,g
PF
,g
FP
are
those adopted in [8].
3R su s
3.1
Effects of Couplings on the Networks Dynamics
Let us start by investigating the synchronization properties of pyramidal neurons
and FS interneurons when the coupling between the two networks is set off. The
corresponding results are reported in figure 1. The left panel shows the results
obtained by setting off the excitatory synapses among pyramidal neurons and the
inhibitory synapses among FS interneurons. In the middle panel are plotted the
results showing as the introduction of coupling modifies the dynamics of both
networks. The excitatory synapses promotes synchronous firing of pyramidal
cells, while the inhibitory coupling among FS interneurons leads to the decrease
of their firing activity.
For the adopted parameter values the increase of the conductance of the in-
hibitory synapses does not significantly improve the synchronization level be-
tween FS cells (data not shown). Instead the increase of the amplitude of the
stimulation current
I
F
of the interneurons leads to a more synchronous network
activity (data not shown). In the right panel of figure 1 are reported the results
obtained with an higher value of the conductance (
g
e
) of the excitatory synapses.
In this case the network of pyramidal cells exhibits a bursting regime. Further
increase of the value of
g
e
determines an enlargement of time windows where the
bursting regime occurs (data not shown). The data on the right panel of figure
1 also show that the presence of the electrical synapses among FS interneurons
promotes an increase of the synchrony of their firing activities.
Let us now start the discussion of the results describing the dynamics of both
networks when the coupling between them is set on. The results reported in the
left panel of figure 2 show that the exitatory synapses (the inhibitory synapses
from FS interneurons to pyramidal neurons are set off) from the pyramidal
cells to the FS interneurons promote a bursting regime in this network (see for
comparison the middle panel of figure 1). In such way the level of synchronous
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