  A network of delay-coupled logistic maps exhibits two different
synchronization regimes, depending on the distribution of the coupling delay
times. When the delays are homogeneous throughout the network, the network
synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92,
144101 (2004)], which may be periodic or chaotic depending on the delay; when
the delays are sufficiently heterogeneous, the synchronization proceeds to a
steady-state, which is unstable for the uncoupled map [Masoller and Marti,
Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from
time-dependent to steady-state synchronization as the width of the delay
distribution increases. We also compare the two transitions to synchronization
as the coupling strength increases. We use transition probabilities calculated
via symbolic analysis and ordinal patterns. We find that, as the coupling
strength increases, before the onset of steady-state synchronization the
network splits into two clusters which are in anti-phase relation with each
other. On the other hand, with increasing delay heterogeneity, no cluster
formation is seen at the onset of steady-state synchronization; however, a
rather complex unsynchronized state is detected, revealed by a diversity of
transition probabilities in the network nodes.
