Abstract
We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ2 on the plane ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.
| Original language | English |
|---|---|
| Pages (from-to) | 1717-1730 |
| Number of pages | 14 |
| Journal | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
| Volume | 12 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2002 Aug |
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Keywords
- Cellular Neural Networks
- Space-dependent template
- Spatial chaos
ASJC Scopus subject areas
- Modelling and Simulation
- Engineering (miscellaneous)
- General
- Applied Mathematics
Cite this
Cellular neural networks : Space-dependent template, mosaic patterns and spatial chaos. / Juang, Jonq; Shieh, Shih Feng; Turyn, Larry.
In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 12, No. 8, 08.2002, p. 1717-1730.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Cellular neural networks
T2 - Space-dependent template, mosaic patterns and spatial chaos
AU - Juang, Jonq
AU - Shieh, Shih Feng
AU - Turyn, Larry
PY - 2002/8
Y1 - 2002/8
N2 - We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ2 on the plane ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.
AB - We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ2 on the plane ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.
KW - Cellular Neural Networks
KW - Space-dependent template
KW - Spatial chaos
UR - http://www.scopus.com/inward/record.url?scp=0036695938&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036695938&partnerID=8YFLogxK
U2 - 10.1142/S0218127402005510
DO - 10.1142/S0218127402005510
M3 - Article
AN - SCOPUS:0036695938
VL - 12
SP - 1717
EP - 1730
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 8
ER -