Higher-order interactions induce stepwise explosive phase transitions

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.