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1.1 Cellular Neural/Nonlinear Network 5
where u kl , x ij , and y kl are the input, the state, and the output variables. A and
B matrices are the feedback and feed-forward templates, and z ij is the bias term.
N r (i,j) is the set of neighboring cells of the (i,j) th cell. The output y ij equation
of the cell is described by the following function (see Figure 1.2):
y ij = f(x ij ) = |x ij + 1| − |x ij − 1|
2
⎧
⎨
=
⎩
1 x ij (t) > 1
x ij (t) −1 ≤ x ij (t) ≤ 1
−1 x ij (t) < −1
(1.2)
f(V xij
)
1
-1
1
V xij
-1
Figure 1.2: The output sigmoid function
The discretized form of the original state equation (1.1) is derived by using
the forward Euler form. It is as follows:
x ij (n + 1)
(
= (1 − h)x ij (n)+
)
∑
∑
+h
A ij,kl y kl (n) + B ij,kl u kl + z ij
C (kl)∈N r(i,j)
C (kl)∈N r(i,j)
(1.3)
In order to simplify computation variables are eliminated as far as possible (e.g.:
combining variables by extending the template matrices). First of all, the Chua-
Yang model is changed to the Full Signal Range (FSR) [20] model. Here the state
and the output of the CNN are equal. In cases when the state is about to go to
saturation, the state variable is simply truncated. In this way the absolute value
of the state variable cannot exceed +1. The discretized version of the CNN state