  In this paper, we report the identification of global and partial phase
synchronizations in linear arrays of unidirectionally coupled piecewise linear
time-delay systems with two different coupling configurations. In particular,
in a linear array with open end boundary conditions, global phase
synchronization (GPS) is achieved by a sequential synchronization as a function
of the coupling strength (a second order transition). 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. On the other hand, in a linear array with closed end boundary
conditions (ring topology), partial phase synchronization (PPS) is achieved by
forming different groups of phase synchronized clusters above some threshold
value of the coupling strength (a first order transition) where they continue
to be in a stable PPS state. We confirm the occurrence of both global and
partial phase synchronizations in two different piecewise linear time-delay
systems using various numerical methods.
