above two systems but with closed end boundary conditions. At first, we use the nonlinear transformation introduced in Senthilkumar [*[et al.,]{}*]{} \[2006, 2008\] to estimate the phase of all the systems in the array and to identify the existence of phase synchronization. Further, we confirm the existence of global phase synchronization (GPS) and partial phase synchronization (PPS) from the original non-phase-coherent hyperchaotic attractors using two independent approaches, namely recurrence quantification analysis [@romano05; @marwan07] and the concept of localized sets [@pereira07]. In addition, we point out that the onset of GPS in the linear array with open end boundary conditions takes place in the form of a sequential synchronization (second order transition): For lower values of coupling strength the phases of nearby systems get already entrained with the drive system in contrast to the far away systems, while the other non-synchronized systems display clusters of phase synchronized states among themselves before they become synchronized with the large cluster in the sequence as the strength of coupling increases to form the GPS.

On the other hand, if we consider an array with closed end boundary conditions (ring topology), partial phase synchronization occurs with the formation of different groups of phase synchronized clusters. 