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Table 2.
Behaviour of the excitatory inhibitory network
I<T
I
Parameters
Convergence
Neuron 1 Neuron 2
T
1
<
W
21
1
−
a
1
(
W
21
1
−
a
1
,
1
,
W
13
+
W
23
)
Spiking
Spiking
1
−
a
3
T
2
<
0
T
1
>
W
21
1
−
a
1
(
W
21
1
−
a
1
,
0
,
W
23
)
Resting
Spiking
1
−
a
3
T
1
<
W
21
1
−
a
1
(
W
21
1
−
a
1
,
1
,
W
13
+
W
23
)
Spiking
Spiking
1
−
a
3
W
21
T
2
>
0
1
−
a
1
<T
1
<
0
Oscillations
T
1
>
0
(0
,
0
,
0)
Resting
Resting
I>T
I
Parameters
Convergence
Neuron 1 Neuron 2
T
1
<
W
I
1
+
W
21
1
−
a
1
(
W
I
1
+
W
21
1
−
a
1
,
1
,
W
13
+
W
23
1
−
a
3
) Spiking
Spiking
T
2
<
0
T
1
>
W
I
1
+
W
21
1
−
a
1
(
W
I
1
+
W
21
1
−
a
1
,
0
,
W
23
1
−
a
3
)
Resting
Spiking
T
1
<
W
I
1
+
W
21
1
−
a
1
(
W
I
1
+
W
21
1
−
a
1
,
1
,
W
13
+
W
23
1
−
a
3
) Spiking
Spiking
T
2
>
0
W
I
1
+
W
21
1
−
a
1
<T
1
<
W
I
1
Oscillations
1
−
a
1
T
1
>
W
I
1
1
−
a
1
(
W
I
1
1
−
a
1
,
0
,
0)
Resting
Resting
loop does. In the other cases, the output value will tend to a fixed point that,
again, depending on the value of the threshold
T
3
, makes the neuron rest or
spike tonically.
4 Experimental Results
To support the model proposed before, we developed a small application in
Python that simulates the network and tested the model with different values of
descent rates, coupling strengths, initial conditions and thresholds that covers
most of the behaviours the model can offer
1
.
In this section we study three of the simulations results in order to illustrate
the values discussed in the previous section. The units used in the graphical
representations are arbitrary. All simulations starts with each neuron inactive
1
The results can be consulted online at: www.ii.uam.es/˜jcano/neuronweb/
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