Study: Do higher-order interactions promote synchronization? sfi_news NatureComms
Fig. 7: Cross-order degree correlation affects synchronization stability in systems with mixed pairwise and nonpairwise interactions , but not in the uniform cases .
The hypergraphs are constructed from the cat brain dataset. For each curve, we indicate the number of pairs of nodes selected for the hyperedge membership swapping procedure . The procedure changes the cross-order degree correlation without affecting the degree sequences . We can see that more negative cross-order degree correlation translates into better synchronization stability.
Do the lessons learned here for phase oscillators carry over to more general oscillator dynamics? The generalized Laplacians used here have been shown to work for arbitrary oscillator dynamics and coupling functions. Moreover, the spread of eigenvalues of each Laplacian carries critical information regarding the synchronizability of the corresponding level of interactions.
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