On the choice of coupling in a system of coupled maps: structure implies features

The conditions of stable synchrony for asymmetrically coupled maps (CM) were analyzed. Utilizing Axlamar´s lemma we derived sufficient conditions for partial pair-wise synchronization. These results allow us to derive the conditions for cluster-to-node and cluster-to-cluster synchronization. We distinguish four particular types of synchronization patterns and analyze their properties. These properties are sensitivity to disturbances and ability of the system to act as either associative memory or classifier. We identify the restrictions on the coupling parameters that determine in which of these models the system operates.