Whether or not periodicity is a property of the environment, for a cognitive system a period is always a dynamical mental construct. This study suggests a dynamical implementation of this hypothesis using recurrent oscillatory self-organizing map of the feature space of such streams. The mapping allows the system to assign identity and class-membership to each stream point, represented by a locus on a two-dimensional map. The model is shown to detect periodicities of various regular and behavior-originated, single- and multi-channel wave patterns, and to reproduce such signals, relying solely on the oscillating activation of the units.