  We report the identification of global phase synchronization (GPS) in a
linear array of unidirectionally coupled Mackey-Glass time-delay systems
exhibiting highly non-phase-coherent chaotic attractors with complex
topological structure. In particular, we show that the dynamical organization
of all the coupled time-delay systems in the array to form GPS is achieved by
sequential synchronization as a function of the coupling strength. Further, the
asynchronous ones in the array with respect to the main sequentially
synchronized cluster organize themselves to form clusters before they achieve
synchronization with the main cluster. We have confirmed these results by
estimating instantaneous phases including phase difference, average phase,
average frequency, frequency ratio and their differences from suitably
transformed phase coherent attractors after using a nonlinear transformation of
the original non-phase-coherent attractors. The results are further
corroborated using two other independent approaches based on recurrence
analysis and the concept of localized sets from the original non-phase-coherent
attractors directly without explicitly introducing the measure of phase.
