Chaotic synchronization on complex hypergraphs

Chaotic synchronization on hypegraphs is studied with chaotic oscillators located in the nodes and with hyperedges corresponding to nonlinear coupling among groups of p   oscillators (p⩾2p⩾2). Using the Master Stability Function approach it can be shown that the problem of stability of the state of identical synchronization for such hypergraphs (called p-hypergraphs) is equivalent to that for a weighted network in which the weights of edges linking pairs of nodes are given by the number of different hyperedges simultaneously connecting these pairs of nodes. As an example, synchronization of identical Lorenz oscillators is investigated on complex scale-free p-hypergraphs. For p even and for a proper choice of the coupling function identical synchronization can be obtained, and the propensity to synchronization depends sensitively on the coupling topology. Besides, such phenomena as partial anti-synchronization, coexistence of the synchronized and oscillation death states with intermingled basins of attraction and quasiperiodic oscillations are observed in numerical simulations.