Lag-mediated control of explosive synchronization transitions in adaptive multilayer networks with higher-order interactions.

Recent findings suggest that higher-order (group) interactions provide a general pathway to explosive phenomena in networks of coupled oscillators. While these abrupt, first-order transitions, termed explosive synchronization, are of significant theoretical interest, they are often undesirable and potentially dangerous in many real-world systems. Motivated by this, we investigate a control mechanism to suppress explosive synchronization in adaptive multilayer networks incorporating higher-order interactions by introducing a phase lag into the system. By appropriately tuning the adaptation exponents and the phase frustration parameter, we demonstrate that phase lag effectively mitigates explosive behavior even in the presence of higher-order interactions, converting the transition from first order to second order. As the phase lag increases, the hysteresis width progressively narrows, and the abrupt transition gives way to a smooth, continuous one. This taming effect remains robust in real-world networks, such as the Macaque brain network. Overall, our study explores an effective control strategy for explosive synchronization and advances our understanding of how critical collective dynamics can be regulated in both synthetic and biological complex systems.