system (Eq. (\[eq\_3pl\])) for the parameter values $\alpha=1.2, \beta=1.0, \tau \in(1,10)$ in the absence of the coupling $\varepsilon$.](threshold_lya){width="0.7\columnwidth"}

\[sec:level3\]Global Phase Synchronization in an Array of Piecewise Linear Systems with Threshold Nonlinear Function
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In this section, we demonstrate the existence of the GPS in another piecewise linear time-delay system with a threshold nonlinear function. This system has been studied recently for its hyperchaotic nature even for small values of time-delay \[see for details, Lakshmanan & Senthilkumar, 2010\] and has also been experimentally realized using analog electronic circuits [@srinivasan11]. Very recently, the chaotic phase synchronization has been experimentally confirmed in this piecewise linear time-delay system along with numerical simulation [@dvs10] and various types of synchronization transitions have been demonstrated both experimentally and numerically in this system [@srinivasan11]. In this paper, we consider a linear array of piecewise linear systems as in Eq. (\[eq\_1\]) and the nonlinear function $f(x)$ is now chosen to be a piecewise linear function with a threshold nonlinearity, $$\label{eq_3pl}
f(x)=AF^{*}-Bx.$$ Here $$\begin{aligned}
F^{*}=
\left\{
\begin{array}{cc}
-x^{*},&  -x < x^{*}  \\
            x,&  -x \leq x \leq x^{*} \\
            x^{*},&  x > x^{*} \\ 
         \end{array} \right.
\label{eq_4}\end{aligned}$$ where $x^{*}$ is a controllable threshold value and $A$ and $B$ are positive 