354
9 Memristor Cellular Neural Networks Computing in the Flux-charge Domain
−
+
−
+
G in
G i2
G i1
R
q Ci 0
C
q Mi 0
h ap (q Mi 0 )
h ap (q Mi (t; t 0 ) + q Mi 0 )
R
C
d
dt
ϕ Ci (t; t 0 )
q Ci (t; t 0 )
q Mi (t; t 0 )
•
•
•
+
−
ϕ u1 (t; t 0 )
+
−
ϕ u2 (t; t 0 )
+
−
ϕ un (t; t 0 )
−
+
ϕ Ci (t; t 0 )
+
−
ϕ Mi (t; t 0 )
+
−
−
+
ϕ Ci (t; t 0 )
−
+
ϕ ui (t; t 0 )
Fig. 9.9 Equivalent circuit of the i-th cell in the (ϕ, q)-domain as obtained via FCAM
The CR of the charge-controlled memristor in the (ϕ, q)-domain is given by
(cf. (9.3))
ϕ M i (t; t 0 ) = −h ap (q M i0 ) + h ap (q M i (t; t 0 ) + q M i0 ).
By substitution we obtain for the 1D NN the following system of n differential
equations in the incremental memristor charges
τ
d
dt
q M i (t; t 0 ) = −q M i (t; t 0 ) +
n
j =1
G ij h ap (q M j (t; t 0 ) + q M j 0 )
−
n
j =1
G ij h ap (q M j 0 ) + q C i0
for i = 1, 2, . . . , n and t ≥ t 0 , where τ = RC is the cell time constant. In terms of
charge we have
τ
d
dt
q M i (t) = −q M i (t) +
n
j =1
G ij h ap (q M j (t)) + q M i0 + q C i0
−
n
j =1
G ij h ap (q M j 0 )
for i = 1, 2, . . . , n and t ≥ t 0 .