TY - JOUR

T1 - Cellular neural networks

T2 - mosaic pattern and spatial chaos

AU - Jonq, Juang

AU - Lin, Song-Sun

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033723714&partnerID=8YFLogxK

U2 - 10.1137/S0036139997323607

DO - 10.1137/S0036139997323607

M3 - Article

AN - SCOPUS:0033723714

SN - 0036-1399

VL - 60

SP - 891

EP - 915

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -