the formation of clusters by the other asynchronous oscillators in the array can be confirmed by plotting their respective generalized autocorrelation functions, which will show that all their maxima are in good agreement with each other, whereas there exists a drift between them and the maxima of the sequentially synchronized cluster as discussed in Ref. [@suresh10].

![image](piece_phase_gaf){width="0.9\columnwidth"}

The global scenario of the existence of GPS via sequential phase synchronization can also confirmed using the index CPR in analogy with the nature of the Kuramoto order parameter $R$, the average frequency difference and the average frequency ratio. The index CPR of the response systems $i=10, 20, 30, 50$ with that of the drive is shown in Fig. \[fig12\] as a function of $\varepsilon$. It is clear that the nearby oscillators to the drive are synchronized first as the coupling strength is gradually increased contributing to the local sequential synchronization. The results are exactly similar to that observed from the average frequency difference and the average frequency ratio in Figs. \[fig8\] indicating the phenomenon of GPS via sequential phase synchronization.

![\[fig12\] Plots of the index CPR as a function of the coupling strength $\varepsilon$. Different lines correspond to the CPR of different 