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a
b
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time (sec)
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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
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x3
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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
 
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