Optimal selection of pinned nodes in heterogeneous higher-order networks

Determine, for heterogeneous higher-order network topologies characterized by first-order adjacency matrix A and second-order adjacency tensor B, the optimal subset of nodes to pin with the proposed feedback control so as to achieve effective desynchronization of the higher-order Kuramoto dynamics.

Background

The paper examines desynchronization via feedback pinning control applied to a subset of nodes M, showing that in all-to-all structures nodes are equivalent, but in general higher-order networks the position of controlled nodes crucially influences control efficacy.

While prior work on pairwise networks links control efficiency to topological features and node centrality, the authors emphasize that for heterogeneous higher-order structures, identifying which nodes to pin is still not established and constitutes an open problem.