On locally regular cellular neural networks

Since their inception, cellular neural networks (CNNs) have been divided into two classes, namely the uncoupled CNNs which do not have intercell feedback and their coupled counterparts which have feedback. The uncoupled class is fully analytically tractable and well understood, whereas the coupled class may exhibit complex dynamics prohibiting an exact analysis. In this paper, the author proposes a different dichotomy by defining the class of locally regular (LR) CNNs which comprises uncoupled and the most commonly used coupled networks. He shows that there is a unifying theory for the design and analysis of this class, and that LR CNNs meet all the requirements for a successful implementation in analog VLSI hardware. In particular, they can be made highly robust against deviations of both template parameters and cells' time constants, and they operate correctly on different classes of CNN chips, including sampled-data implementations and networks with high-gain or hardlimiting output nonlinearity. Furthermore, they can be numerically simulated very efficiently, since the integration step size may be chosen as large as the cell's time constant.