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a
b
8
80
60
6
40
4
20
2
0
0
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−2
−40
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−60
−6
−80
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5
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0
5
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time (sec)
time (sec)
Fig. 4.13 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
50
1
0.2
0
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0
−0.2
−1
−50
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x1
time (sec)
time (sec)
50
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time (sec)
time (sec)
x3
Fig. 4.14 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 )
4.14
Conclusions
A new method for robust synchronization of coupled neural oscillators has been
developed. The model of the FitzHugh-Nagumo neural oscillators has been con-
sidered which represents efficiently voltage variations on the neuron's membrane,
due to ionic currents and external activation currents. It was pointed out that
synchronism between the coupled neurons is responsible for rhythm generation
and control of several functions in living species such as gait, breathing, heart's
pulsing, etc. Moreover, models of synchronized neurons can be used in several
robotic applications to control locomotion of multilegged, quadruped, and biped
robots.
 
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