Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 66, Issue 12, Pages 6100-6107Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3062005
Keywords
Kuramoto oscillators; networks of networks; partial synchronization
Funding
- European Research Council [ERC-CoG-771687]
- Netherlands Organization for Scientific Research [NWO-vidi-14134]
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Partial synchronization in brain networks can be induced by strong regional connections in coupled subnetworks of Kuramoto oscillators, with critical values for algebraic connectivity and node strength determining the conditions for partial phase cohesiveness. This study presents the first known criterion based on the incremental 8-norm for noncomplete graphs, and highlights the interplay between anatomical structure and empirical patterns of synchrony in real anatomical brain network data through numerical simulations.
Partial, instead of complete, synchronization has been widely observed in various networks, including, in particular, brain networks. Motivated by data from human brain functional networks, in this article, we analytically show that partial synchronization can be induced by strong regional connections in coupled subnetworks of Kuramoto oscillators. To quantify the required strength of regional connections, we first obtain a critical value for the algebraic connectivity of the corresponding subnetwork using the incremental two-norm. We then introduce the concept of the generalized complement graph, and obtain another condition on the node strength by using the incremental 8-norm. Under these two conditions, regions of attraction for partial phase cohesiveness are estimated in the forms of the incremental two- and 8-norms, respectively. Our result based on the incremental 8-norm is the first known criterion that applies to noncomplete graphs. Numerical simulations are performed on a two-level network to illustrate our theoretical results; more importantly, we use real anatomical brain network data to show how our results may contribute to a better understanding of the interplay between anatomical structure and empirical patterns of synchrony.
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