Humans are able to perform a large variety of periodic activities in different modes, for instance cyclic rehearsal of phone numbers, humming a melody sniplet over and over again. These performances are, to a certain degree, robust against perturbations, and it often suffices to present a new pattern a few times only until it can be "picked up". From an abstract mathematical perspective, this implies that the brain, as a dynamical system, (1) hosts a very large number of cyclic attractors, such that (2) if the system is driven by external input with a cyclic motif, it can entrain to a closely corresponding attractor in a very short time. This chapter proposes a simple recurrent neural network architecture which displays these dynamical phenomena. The model builds on echo state networks (ESNs), which have recently become popular in machine learning and computational neuroscience.