Analysis of synchronization transitions in higher-order Kuramoto oscillator system with different orders of phase lags

Phase lag plays a crucial role in the modeling and understanding of various complex systems. In this work, two phase lags acting on different orders of coupling are introduced in Kuramoto oscillator system. Based on a low-dimensional model, theoretical analysis precisely reveals that increasing the phase lag associated with the pairwise coupling does not alter the synchronization transition mode but shifts both the saddle-node and subcritical bifurcation points. Moreover, it leads to an expansion of the hysteresis width during explosive synchronization. In contrast, increasing the phase lag related to the 2-simplex coupling progressively reduces the hysteresis width until the system exhibits a continuous synchronization transition. These conclusions are also verified in two empirical networks, where a network with higher average 2-simplex degree is more likely to induce explosive synchronization and wider hysteresis region.