Explosive synchronization in a mobile network in the presence of a positive feedback mechanism

Synchronization is a process that describes the coherent dynamics of a large ensemble of interacting units. The study of explosive synchronization transition attracts considerable attention. Here, I report the explosive transition within the framework of a mobile network, while each oscillator is controlled by global-order parameters of the system. Using numerical simulation, I find that the explosive synchronization (ES) transition behavior can be controlled by simply adjusting the fraction of controlled oscillators. The influences of some parameters on explosive synchronization are studied. Moreover, due to the presence of the positive feedback mechanism, I prevent the occurrence of the synchronization of continuous-phase transition and make phase transition of the system a first-order phase transition accompanied by a hysteresis loop.