Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions

In this paper the problem of the stability of Cellular Neural Networks (CNN´s) and Delayed Cellular Neural Networks (DCNN´s) is addressed by means of Lyapunov functions (functionals in the delayed case); new classes of nonpositive templates, describing CNN´s and DCNN´s, are shown to be stable and some conditions are found ensuring the complete stability of dominant template DCNN´s and CNN´s with nonmonotonic output functions.