Synchronization in Multiplex Systems with Simplex Interactions Beyond All-to-All Coupling

We investigate syncrhonization transitions in the networks with higher-order symplectic interactions beyond the paradigm of global coupling. In particular, we consider sparse random pairwise and triadic coupling in phase oscillator networks, and additionally address the effect of multiplexing to the layer with the regular grid architecture. We demonstrate the persistence of the first order transition to synchronization in the case of sparse coupling, and find that the regular grid can induce such transition even when the pairwise coupling strength is insufficient. Surprisingly, we also find temporary desynchronization that becomes possible also due to multiplexing to the grid of oscillators.