Biomedical Engineering Reference
In-Depth Information
Figure 6. A circuit representation of a simple OBB module
max( , )
gcd( ,
r r
sary. Thus we have,
i
j
(1)
=
i
r
+ −
r
r r
)
i
j
i
j
M
(
k
+ =
1)
M
( )
k
+
w v
( )
k
+
w v
( )
k
i
i
ji
j
ii
i
max( ,
r r
)
i
j
(2)
w
=
M
(
k
+ =
1)
M
( )
k
+
w v
( )
k
+
w v
( )
k
ij
'
j
j
ij
i
jj
j
r
(5)
min( ,
r r
)
gcd( ,
r r
)
i
j
i
j
(3)
=
where,
j
r
+ −
r
gcd( ,
r r
)
i
j
i
j
v
( )
k
=
max(0,sgn(
M
( )
k
))
min( ,
r r
)
i
i
i
(4)
i
j
w
=
(6)
ji
v
( )
k
=
max(0,sgn(
M
( )
k
))
'
r
j
j
j
We arrange the system parameters by compar-
ing two nodes' reversibilities. If r i > r j , then we
have θ i > θ j and w ij > w j , i.e., a node with smaller
reversibility, corresponding to a neuron with lower
threshold in an OBB module, will oscillate at a
higher frequency than its companion does. This
arrangement scheme ensures that the behaviour of
SMER-based OBB modules is consistent with its
original SMER algorithm. The difference equation
in the discrete time domain of this system can be
formulated as follows: each neuron's self-feedback
strength is w ii = - w ij , w ij = - w ji , respectively, and
the activation function is a sigmoid Heaviside
type. It is worth noticing that k is the local clock
pulse of each neuron, a global clock is not neces-
We consider the designed circuit as a conser-
vative dynamical system in an ideal case. The
total energy is constant, no loss or complement
is allowed. The sum of two cells' postsynaptic
potential at any given time is normalised to one.
It is clear that this system has the capability of
self-organised oscillation with the firing rate of
each neuron arbitrarily adjustable. However, like
most dynamic systems, our model has a limit in
its dynamic range. There exists a singular point
as each cell's postsynaptic potential equals to its
threshold; in this case, the system may transit to
another different oscillation behaviour or even
halt. Within its normal dynamic range, the fol-
 
Search WWH ::




Custom Search