Influence of boundary conditions on the behavior of cellular neural networks

Every cell of a cellular neural network (CNN) has the same neighborhood, except if it is located on an edge of the array forming the finite-sized network. Boundary conditions can be introduced to complete the neighborhood of these cells. It is shown that the dynamical behavior of an important group of cellular neural networks strongly depends on these boundary conditions: some boundary conditions make the network stable whereas other make it unstable. There also exist CNNs that are unstable regardless of the boundary conditions. The instability of the CNNs of the first group is due to an external cause (their boundary conditions), while the instability of the networks of the second group is proper to the template that defines them