Enhanced explosive synchronization in heterogeneous oscillator populations with higher-order interactions

Explosive synchronization underlying many realistic dynamic processes has attracted great attention in the various fields. Here, we generalize the Kuramoto model with heterogeneous coupling incorporating the higher-order interactions encoded with the simplicial complexes. We show that the introduced nonlinear couplings can significantly enhance the emergence of explosive synchronization in addition to the pairwise interactions. In particular, we uncover that the critical thresholds manifesting the onset or vanishing of the abrupt synchronization are enlarged as the fraction of the higher-order interactions increases. As a consequence, the backward critical order parameter characterizing the desynchronization transition and the width of hysteresis supporting the bistability are remarkably improved. More importantly, we provide an analytical treatment for untangling the stability properties of the equilibrium states at different levels, which allows us to understand the bifurcation mechanism and locate the associated critical points. This study is a step forward in highlighting the importance of higher-order interactions among dynamical units, which might provide control strategies for the induced abrupt emergent phenomena in networked system.