Discontinuous Transitions and Rhythmic States in the D-Dimensional Kuramoto Model Induced by a Positive Feedback with the Global Order Parameter.

  title={Discontinuous Transitions and Rhythmic States in the D-Dimensional Kuramoto Model Induced by a Positive Feedback with the Global Order Parameter.},
  author={Xiangfeng Dai and Xuelong Li and H. Guo and D R Jia and Matja{\vz} Perc and Pouya Manshour and Zhen Wang and Stefano Boccaletti},
  journal={Physical review letters},
  volume={125 19},
From fireflies to cardiac cells, synchronization governs important aspects of nature, and the Kuramoto model is the staple for research in this area. We show that generalizing the model to oscillators of dimensions higher than 2 and introducing a positive feedback mechanism between the coupling and the global order parameter leads to a rich and novel scenario: the synchronization transition is explosive at all even dimensions, whilst it is mediated by a time-dependent, rhythmic, state at all… Expand

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