'$^2$Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany'
- '$^3$Institute of Physics, Humboldt University, 12489 Berlin, Germany'
- '$^4$Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom'
author:
- 'R. Suresh$^{1}$, D. V. Senthilkumar$^{2}$, M.  Lakshmanan$^{1,}$[^1], and J. Kurths$^{2,3,4}$'
title: 'GLOBAL AND PARTIAL PHASE SYNCHRONIZATIONS IN ARRAYS OF PIECEWISE LINEAR TIME-DELAY SYSTEMS'
---

\[sec:level1\]Introduction
==========================

Chaotic phase synchronization (CPS) associated with a locking of the phases of coupled chaotic systems corresponds to the case where the amplitudes are still uncorrelated. CPS has been investigated in ensembles of globally coupled arrays [@pikovsky01; @boccaletti02; @ivanchenko04; @takamatsu00; @pikovsky96; @kiss02; @zhou02; @osipov97; @zhan00; @kozyreff00; @otsuka06], networks of oscillators [@boccaletti06; @arenas08; @batista07; @ren07; @yu09], laser systems [@kozyreff00; @otsuka06], cardiorespiratory systems [@schafer09; @stefanovska00; @bartsch07], ecology [@blasius99; @sismondo90; @amritkar06], climatology [@rybski06; @yamasaki09; @maraun05], etc. CPS is well studied and understood in low dimensional systems; however, there exist a very little indepth studies in higher dimensional systems such as time-delay systems, which are essentially infinite-dimensional and exhibit highly non-phase-coherent hyperchaotic attractors with complex topological structures. So estimating the phase explicitly to identify phase synchronization in such systems is quite difficult. Recently, the occurrence of phase synchronization in time-delay systems has been 