Cellular Neural Networks : Mosaic Pattern and Spatial Chaos

@inproceedings{SIAMJ2000CellularNN,
  title={Cellular Neural Networks : Mosaic Pattern and Spatial Chaos},
  author={A SIAMJ.},
  year={2000}
}
  • A SIAMJ.
  • Published 2000
We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z 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… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 36 extracted citations

Piecewise Two-Dimensional Maps and Applications to Cellular Neural Networks

I. J. Bifurcation and Chaos • 2004
View 5 Excerpts
Highly Influenced

The Spatial Complexity of Inhomogeneous Multi-layer Neural Networks

Neural Processing Letters • 2014
View 6 Excerpts
Highly Influenced

Spatial complexity in multi-layer cellular neural networks

2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010) • 2010
View 4 Excerpts
Highly Influenced

Abundance of Mosaic Patterns for CNN with Spatially Variant Templates

I. J. Bifurcation and Chaos • 2002
View 4 Excerpts
Highly Influenced

On the Spatial Entropy and Patterns of Two-Dimensional Cellular Neural Networks

I. J. Bifurcation and Chaos • 2002
View 5 Excerpts
Highly Influenced

Cellular Neural Networks: Mosaic Patterns, bifurcation and Complexity

I. J. Bifurcation and Chaos • 2006
View 4 Excerpts
Highly Influenced

Deep and Shallow Architecture of Multilayer Neural Networks

IEEE Transactions on Neural Networks and Learning Systems • 2015
View 1 Excerpt

References

Publications referenced by this paper.
Showing 1-10 of 39 references

Pattern formation properties of autonomous cellular neural networks

P. Thiran, K. R. Crounse, L. O. Chua, M. Hasler
IEEE Trans. Circuits Systems, 42 • 1995
View 9 Excerpts
Highly Influenced

Threshold behavior and propagation for nonlinear differentialdifference systems motivated by modeling myelinated axons

J. Bell, C. Cosner
Quart. Appl. Math., 42 • 1984
View 7 Excerpts
Highly Influenced

Some threshold results for modes of myelinated nerves

J. Bell
Math. Biosci., 54 • 1981
View 7 Excerpts
Highly Influenced

Theory of crystal growth and interface motion in crystalline materials

J. W. Cahn
Acta Metallurgica, 8 • 1960
View 9 Excerpts
Highly Influenced

Chaos of traveling waves in a discrete chain of diffusively coupled maps

V. S. Afraimovich, V. I. Nekorkin
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 4 • 1994
View 7 Excerpts
Highly Influenced

The CNN paradigm

View 4 Excerpts
Highly Influenced

Pattern formation and spatial chaos for cellular neural networks with asymmetric templates

C. W. Shih
Internat. J Bifur. Chaos Appl. Sci. Engrg., 8 • 1998
View 1 Excerpt

Pattern formation and spatial chaos for cellular neural networks with asymmetric templates , Internat

C. W. Shih
J Bifur . Chaos Appl . Sci . Engrg . • 1998

Similar Papers

Loading similar papers…