Unveiling the birth of explosive entrainment: A novel phenomenon triggered by higher-order interactions.

Entrainment is an important collective behavior in complex networks, where the output period of the coupled neuronal oscillator matches the external input period and maintains a stable phase relationship. The typical feature of entrainment is the regions in the input period and input amplitude parameter space, known as the Arnold tongue. In this article, we introduced a higher-order Kuramoto model and found that the transition process of the coupled neuronal oscillators from the unentrainment state to the entrainment state is a discontinuous first-order phase transition process accompanied by the hysteresis phenomenon. Interestingly, this discontinuous first-order phase transition process results in the appearance of two Arnold tongue structures in the parameter space. Our results provide more insights into the emergence of the explosive entrainment and have been confirmed by the theoretical analysis.