PPKE ITK PhD and MPhil Thesis Classes

4 1. INTRODUCTION
1.1 Cellular Neural/Nonlinear Network
The basic building blocks of the Cellular Neural Networks, which was published in
1988 by L. O. Chua and L. Yang [17], are the uniform structured analog processing
elements, the cells. A standard CNN architecture consists of a rectangular 2Darray
of cells as shown in Figure (1.1). With interconnection of many 2D arrays
it can be extended to a 3-dimensional, multi-layer CNN structure. As it is in
organic structures the simplest way to connect each cell is the connection of
the local neighborhood via programmable weights. The weighted connections of
a cell to its neighbors are called the cloning template. The CNN cell array is
programmable by changing the cloning template. With the local connection of
the cells difficult computational problems can be solved, like modeling biological
structures [18] or the investigation of the systems which are based on partial
differential equations [19].
Figure 1.1: Location of the CNN cells on a 2D grid, where the gray cells are the
direct neighbors of the black cell
1.1.1 Linear templates
The state equation of the original Chua-Yang model [17] is as follows:
∑
∑
ẋ ij (t) = −x ij + A ij,kl y kl (t) + B ij,kl u kl + z ij (1.1)
C (kl)∈N r(i,j)
C (kl)∈N r(i,j)