Cellular neural networks: mosaic pattern and spatial chaos

Juang Jonq, Song-Sun Lin

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z2 on the plane R2. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and ε, 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; ε) can be completely characterized. This, in turn, addresses the so-called learning problem in CNNs. The complexities of mosaic patterns are also addressed.

Original languageEnglish
Pages (from-to)891-915
Number of pages25
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 1 Jan 2000

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