Design and synthesis methods for cellular neural networks

Cellular neural networks (CNN) are described by large systems of locally coupled nonlinear differential equations. In most applications the connectivity are specified through space-invariant templates. As far as the dynamic behavior is concerned, CNNs can be divided in two main classes: stable CNNs, with the property that each trajectory (with exception of a set of measure zero) converges towards an equilibrium point; unstable CNNs, that exhibit at least one attractor, that is not a stable equilibrium point. Due to their complex dynamics, only a few methods for template design have been so far proposed. We propose a rigorous design algorithm for stable CNNs and we identify the class of templates to which such an algorithm can be applied.