Entrainment of randomly coupled oscillator networks by periodic external
forcing applied to a subset of elements is numerically and analytically
investigated. For a large class of interaction functions, we find that the
entrainment window with a tongue shape becomes exponentially narrow for
networks with higher hierarchical organization. However, the entrainment is
significantly facilitated if the networks are directionally biased, i.e.,
closer to the feedforward networks. Furthermore, we show that the networks with
high entrainment ability can be constructed by evolutionary optimization
processes. The neural network structure of the master clock of the circadian
rhythm in mammals is discussed from the viewpoint of our results.Comment: 15 pages, 11 figures, RevTe