Cellular neural networks: Mosaic patterns, bifurcation and complexity

Abstract

We study a one-dimensional Cellular Neural Network with an output function which is nonflat at infinity. Spatial chaotic regions are completely characterized. Moreover, each of their exact corresponding entropy is obtained via the method of transition matrices. We also study the bifurcation phenomenon of mosaic patterns with bifurcation parameters z and beta. Here z is a source (or bias) term and beta is the interaction weight between the neighboring cells. In particular, we find that by in.jecting the source term, i.e. z not equal 0,a lot of new chaotic patterns emerge with a smaller interaction weight beta. However, as beta increases to a certain range, most of previously observed chaotic patterus disappear, while other new chaotic patterns emerge.