Cellular Neural Networks: Mosaic Pattern and Spatial Chaos
Jonq Juang, Song-Sun Lin · SIAM Journal on Applied Mathematics · 2000
We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z 2 on the plane R 2 . We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and $\varepsilon$, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic patterns and the parameter space $(z,a;\varepsilon)$ can be completely characterized. This, in turn, addresses the so-called learning problem in CNNs. The complexities of mosaic patterns are also addressed.