The transition to synchronization of networked systems

Atiyeh Bayani, Fahimeh Nazarimehr, Sajad Jafari (), Kirill Kovalenko, Gonzalo Contreras-Aso, Karin Alfaro-Bittner (), Rubén J. Sánchez-García () and Stefano Boccaletti
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Atiyeh Bayani: Amirkabir University of Technology (Tehran Polytechnic)
Fahimeh Nazarimehr: Amirkabir University of Technology (Tehran Polytechnic)
Sajad Jafari: Amirkabir University of Technology (Tehran Polytechnic)
Kirill Kovalenko: School for Advanced Studies
Gonzalo Contreras-Aso: Calle Tulipán s/n
Karin Alfaro-Bittner: Calle Tulipán s/n
Rubén J. Sánchez-García: University of Southampton
Stefano Boccaletti: CNR - Institute of Complex Systems

Nature Communications, 2024, vol. 15, issue 1, 1-11

Abstract: Abstract We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network’s nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.

Date: 2024
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DOI: 10.1038/s41467-024-48203-6

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