Taming cluster synchronization

Synchronization is a widespread phenomenon observed across natural and artificial networked systems. It often manifests itself by clusters of units exhibiting coincident dynamics. These clusters are a direct consequence of the organization of the Laplacian matrix eigenvalues into spectral localized blocks. We show how the concept of spectral blocks can be leveraged to design straightforward yet powerful controllers able to fully manipulate cluster synchronization of a generic network, thus shaping at will its parallel functioning. Specifically, we demonstrate how to induce the formation of spectral blocks in networks where such structures would not exist, and how to achieve precise mastering over the synchronizability of individual clusters by dictating the sequence in which each of them enters or exits the synchronization stability region as the coupling strength varies. Our results underscore the pivotal role of cluster synchronization control in shaping the parallel operation of networked systems, thereby enhancing their efficiency and adaptability across diverse applications.