  Non-Markovian evolution of an open quantum system can be induced by the
memory effects of a reservoir. Although a reservoir with stronger memory
effects may seem like it should cause stronger non-Markovian effects on the
system of interest, this seemingly intuitive thinking may not always be
correct. We illustrate this by investigating a qubit (a two-level atom) that is
coupled to a hierarchical environment, which contains a single-mode cavity and
a reservoir consisting of infinite numbers of modes. We show how the
non-Markovian character of the system is influenced by the coupling strength
between the qubit and cavity and the correlation time of the reservoir. In
particular, we found a new phenomenon whereby the qubit Markovian and
non-Markovian transition exhibits a anomalous pattern in a parameter space
depicted by the coupling strength and the correlation time of the reservoir.
