Synchronization transition induced in a partial resetting oscillator system with adaptive coupling

Explosive synchronization has gained significant attention due to its potential applications in understanding complex dynamic systems. This study systematically examines the impacts of partial resetting and adaptive coupling on the synchronization transition in globally coupled Kuramoto oscillators by employing the self-consistent equation and Ott-Antonsen ansatz under three scenarios. The critical coupling strength is determined by the stability of the incoherent solution. Near the critical coupling strength, perturbation analysis reveals that a sufficient resetting proportion is key to inducing explosive synchronization. A non-zero mean of the oscillator's natural frequency distribution is the next dominant factor of explosive synchronization. Increasing the resetting frequency shrinks the hysteresis region, which may ultimately yield a continuous transition. The numerical simulations align well with theoretical analysis.