attractors, to confirm the existence of GPS in the array of coupled time-delay systems, both qualitatively and quantitatively.

A criterion to quantify phase synchronization between two systems is the Correlation of Probability of Recurrence (CPR) defined as $$\begin{aligned}
CPR=\langle \bar{P_1}(t)\bar{P_2}(t)\rangle/\sigma_1\sigma_2,
\label{cpr}\end{aligned}$$ where $P(t)$ is the recurrence-based generalized autocorrelation function defined as $$P(t)=\frac{1}{N-t} \sum_{i=1}^{N-t} \Theta(\epsilon-||X_i-X_{i+t}|| ),$$ where $\Theta$ is the Heaviside function, $X_i$ is the $i^{th}$ data point of the system $X$, $\epsilon$ is a predefined threshold, $|| . ||$ is the Euclidean norm, and $N$ is the number of data points, $\bar{P}_{1,2}$ means that the mean value has been subtracted and $\sigma_{1,2}$ are the standard deviations of $P_1(t)$ and $P_2(t)$, respectively. Looking at the coincidence of the positions of the maxima of $P(t)$ of the coupled systems, one can qualitatively identify PS [@romano05; @marwan07]. If both systems are in CPS, the probability of recurrence is maximal at the same time $t$ and CPR $\approx 1.0$. If they are not in CPS, the maxima do not occur simultaneously and hence one can expect a drift in both probabilities of recurrences resulting in low values of CPR.

\[ls\] The concept of localized sets
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Another measure that we have employed is the 