Turyn, Larry Cellular neural networks: asymmetric space-dependent templates, mosaic patterns, and spatial chaos. (English) Zbl 1129.37312 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 8, 2655-2665 (2004). 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) Keywords:Cellular Neural Networks; asymmetric space-dependent templates; spatial chaos PDFBibTeX XMLCite \textit{L. Turyn}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 8, 2655--2665 (2004; Zbl 1129.37312) 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.