Suppression of explosive synchronization in adaptive Kuramoto oscillators with higher-order interactions
Adaptive higher-order interactions among coupled dynamical systems have found widespread applications in real-world systems. Such interactions are known to drive the system into an explosive first-order transition to synchronization. We employ a generalized adaptation function of the global order parameter to modulate the coupling strengths in a Kuramoto model with pairwise and triadic interactions, and to show that the adaptation exponents act as control parameters capable of suppressing explosive synchronization and reshaping the nature of the transition. We derive a self-consistency equation governing the dynamics of the system to determine the critical conditions for the onset of synchronization through the Ott-Antonsen ansatz. We find that positive adaptive exponents drive the system into an explosive first-order transition to synchronization, while negative exponents suppress it, steering the system toward a continuous second-order transition. All analytical predictions are validated through direct numerical simulations. Our results may be useful in understanding and controlling the nature of synchronization transitions in real-world systems where higher-order interactions and adaptive feedback coexist.