×

Cellular neural networks: asymmetric space-dependent templates, mosaic patterns, and spatial chaos. (English) Zbl 1129.37312

Summary: We consider a Cellular Neural Network (CNN), with a bias term, on the integer lattice \(\mathbb Z^2\) in the plane \(\mathbb R^2\). Space-dependent, asymmetric couplings (templates) appropriate for CNN in the hexagonal lattice on \(\mathbb R^2\) are studied. We characterize the mosaic patterns and study their spatial entropy. It appears that for this problem, asymmetry of the template has a more robust effect on the spatial entropy than does the sign of a parameter in the templates.

MSC:

37C99 Smooth dynamical systems: general theory
33C20 Generalized hypergeometric series, \({}_pF_q\)
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37B15 Dynamical aspects of cellular automata
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
68T10 Pattern recognition, speech recognition
68Q80 Cellular automata (computational aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1109/81.989168 · doi:10.1109/81.989168
[2] DOI: 10.1109/81.473583 · doi:10.1109/81.473583
[3] Chow S.-N., Rand. Comput. Dyn. 4 pp 109–
[4] DOI: 10.1142/S0218127496000977 · Zbl 1005.39504 · doi:10.1142/S0218127496000977
[5] DOI: 10.1109/31.7600 · Zbl 0663.94022 · doi:10.1109/31.7600
[6] DOI: 10.1109/31.7601 · doi:10.1109/31.7601
[7] DOI: 10.1109/81.222795 · Zbl 0800.92041 · doi:10.1109/81.222795
[8] DOI: 10.1007/3-540-58843-4_14 · doi:10.1007/3-540-58843-4_14
[9] DOI: 10.1142/9789812798589 · doi:10.1142/9789812798589
[10] DOI: 10.1142/S0218127496001053 · Zbl 0881.92008 · doi:10.1142/S0218127496001053
[11] DOI: 10.1142/S0218127400001031 · Zbl 1090.34561 · doi:10.1142/S0218127400001031
[12] DOI: 10.1137/S0036139997323607 · Zbl 0947.34038 · doi:10.1137/S0036139997323607
[13] Juang J., Int. J. Bifurcation and Chaos 10 pp 2845–
[14] DOI: 10.1142/S0218127402005510 · Zbl 1044.37008 · doi:10.1142/S0218127402005510
[15] DOI: 10.1142/S0218127402004206 · Zbl 1064.34512 · doi:10.1142/S0218127402004206
[16] DOI: 10.1109/81.473584 · doi:10.1109/81.473584
[17] DOI: 10.1002/cta.195 · Zbl 1013.68168 · doi:10.1002/cta.195
[18] DOI: 10.1142/S0218127498001601 · Zbl 1002.92512 · doi:10.1142/S0218127498001601
[19] DOI: 10.1137/S0036139998340650 · Zbl 0985.37091 · doi:10.1137/S0036139998340650
[20] DOI: 10.1109/81.473585 · doi:10.1109/81.473585
[21] Thiran P., Dynamics and Self-Organization of Locally Coupled Neural Networks (1997) · Zbl 0879.68091
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.