Generalized adaptation-induced non-universal synchronization transitions in random hypergraphs

We investigate the effect of partial order parameter adaptation in the form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are considered pairwise and triangular. Using the Ott–Antonsen ansatz, we obtain a set of self-consistent equations of the order parameter that describe the synchronization patterns. A broad diversity of synchronization transitions is observed as a result of the interplay between the partial adaptation approach, generalized adaptation functions, and coupling strengths. The system specifically shows a double-jump transition under a power law form of the adaptation function. A polynomial form of the adaptation function leads to the emergence of an intermediate synchronization state for specific combinations of one negative and one positive coefficient. Moreover, the synchronization transition may become continuous or explosive when the pairwise coupling strength varies. This type of synchronization behavior is further found by using a Gaussian adaptation function.