\[fig:criticality\] shows that behaviour of the order parameter as a function of the coupling. The rich-club undergoes a transition to burst synchronization at $\Delta \alpha \approx 0.4$ that corresponds to an increase of roughly $40\%$ of the coupling strength and is close to the predicted value $\Delta \alpha \approx 0.42$. In the Supplementary Materials, we present other examples where the local dynamics is fully chaotic.

[0.9]{} ![[**Prediction of critical transitions in the rich-club of the cat cerebral cortex.**]{} The level of average synchronization $r$ of the rich-club is shown for different values of the coupling strength. Insets show time series of neuronal dynamics of four rich-club members and color of time series matches with the color of nodes in Fig. \[RC2\]. For values in the grey shaded region, $r$ is increasing towards close to one and the rich-club exhibits collective behavior. We can predict the critical coupling $\alpha_c$ with some standard deviation (grey shaded region) by studying the effective network obtained from a time series measured when $\Delta \alpha=0.3$.[]{data-label="fig:criticality"}](alpha_vs_r_v2-01.png "fig:"){width="0.9\linewidth"}

Obtaining a statistical description of the network {#obtaining-a-statistical-description-of-the-network .unnumbered}
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The effective network can also provide detailed information on the structure of each community and a statistical description of the 