Biomedical Engineering Reference
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Figure 8. The second component of the state x 2 (t), for the forced system
Figure 9. Time evolution of the state's components for the unforced system
Theorem 7. Consider the Hopfield-type neural
network with time-delays (24) under the following
assumptions:
3. the delays are sufficiently small satisfying
( )
min
a
=
max
i
i
i
+
m
m
m
m
1
L
max
c
L
a
+
c
k
ij
j
j
jk
j
1
1
1
1
1.
the nonlinearities f i are of the sigmoidal
type, what means they are non-decreasing,
odd and restrict to the first and third quad-
rants;
(45)
Then the network (24) has a gradient-like
behavior as well as the network (5).
2.
the synaptic weight c ij are such that they
describe a doubly dominant matrix, i.e.,
they satisfy
“Small delays don't matter” is an occasional
remark of Jaroslav Kurzweil regarding the pres-
ervation of various properties of the dynamical
systems for small delays—and it is also the con-
c
c
,
c
c
;
ii
ki
kk
ki
k
i
i
k
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