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a
b
6
60
50
5
40
4
30
3
20
2
10
1
0
0
−10
−1
−20
−2
−30
0
5
10
15
20
25
30
35
40
0
5
10
15
20
25
30
35
40
time (sec)
time (sec)
Fig. 4.9
Synchronization in the model of the two coupled FitzHugh-Nagumo neurons (
a
) between
state variables x
1
(master neuron) and x
3
(slave neuron), (
b
) between state variables x
2
(master
neuron) and x
4
(slave neuron)
a
b
5
1
0.2
0
0
0
−0.2
−5
−1
10
20
30
40
10
20
30
40
−1.5
−1
−0.5
0
0.5
1
1.5
x1
time (sec)
time (sec)
4
5
0.5
2
0
0
0
−2
−0.5
−5
−4
−1.5
−1
−0.5
0
0.5
1
1.5
10
20
30
40
10
20
30
40
x3
time (sec)
time (sec)
Fig. 4.10
Phase diagrams of the synchronized FitzHugh-Nagumo neurons (
a
) between state
variables x
1
-x
2
(master neuron) and between x
3
-x
4
(slave neuron), (
b
) estimation of disturbances
affecting the master neuron (state variables
z
5
and
z
6
) and the slave neuron (state variables
z
7
and
z
8
)
The results obtained in the first test case are shown in Figs.
4.9
and
4.10
. The results
obtained in the second case are shown in Figs.
4.11
and
4.12
. Finally, the results
obtained in the third case are shown in Figs.
4.13
and
4.14
.
In Figs.
4.9
a,
4.11
a, and
4.13
a it is shown how the proposed Kalman Filter-
based feedback control scheme succeeded the convergence of state variable x
1
of
the master neuron to state variable x
3
of the second neuron. Similarly, in Figs.
4.9
b,
4.11
b, and
4.13
b it is shown how the proposed Kalman Filter-based feedback control
scheme succeeded the convergence of state variable x
2
of the master neuron to state
variable x
3
of the second neuron. In Figs.
4.10
a,
4.12
a, and
4.14
a the phase diagrams
between the state variables x
1
, x
2
of the master neuron and the phase diagrams
between the state variables x
3
, x
4
of the slave neuron are presented. The phase
diagrams for the master and slave neuron become identical and this is an indication