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Explosive or Continuous: Incoherent state determines the route to synchronization

Explosive or Continuous: Incoherent state determines the route to synchronization

Abstract Abrupt and continuous spontaneous emergence of collective synchronization of coupled oscillators have attracted much attention. In this paper, we propose a dynamical ensemble order parameter equation that enables us to grasp the essential low-dimensional dynamical mechanism of synchronization in networks of coupled oscillators. Different solutions of the dynamical ensemble …