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

Abstract

The cellular neural networks with two kinds of two-parametered asymmetric templates are considered. The parameter space is partitioned into finitely many disjoint regions. In each region, the basic mosaic patterns are characterized. The feasible mosaic patterns corresponding to the parameters in each region can then be determined. To exhibit the spatial complexity of the system, we estimate the entropy of mosaic patterns for parameters in the regime of spatial chaos. In light of this characterization, the effect from the symmetry of the template on pattern formation properties can be seen in detail. We also discuss the existence of some fundamental class of feasible local defect patterns. It is shown that the feasible local k-defect patterns of vertical type cannot exist if the connection weights are anti-symmetric in the vertical direction. Same conclusion also holds for the ones of horizontal type and horizontal direction.