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

@article{Dai2020DiscontinuousTA,
  title={Discontinuous Transitions and Rhythmic States in the D-Dimensional Kuramoto Model Induced by a Positive Feedback with the Global Order Parameter.},
  author={X. Dai and X. Li and H. Guo and D. Jia and M. Perc and P. Manshour and Z. Wang and S. Boccaletti},
  journal={Physical review letters},
  year={2020},
  volume={125 19},
  pages={
          194101
        }
}
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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References

SHOWING 1-10 OF 80 REFERENCES
Continuous versus Discontinuous Transitions in the $D$-Dimensional Generalized Kuramoto Model: Odd $D$ is Different
The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior ofExpand
Exact results for the Kuramoto model with a bimodal frequency distribution.
TLDR
This work derives the system's stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians and shows that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Expand
The Kuramoto model in complex networks
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The mostExpand
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certainExpand
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
Abstract Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, theseExpand
Synchronization and Bellerophon states in conformist and contrarian oscillators
TLDR
Two populations of globally coupled conformist and contrarian oscillators are considered, and a novel non-stationary state is identified which is essentially different from all other coherent states previously reported in the Literature. Expand
Explosive synchronization in adaptive and multilayer networks.
TLDR
This work shows that explosive synchronization of networked oscillators is far more general and can occur in adaptive and multilayer networks in the absence of such correlation properties, and provides a rigorous, analytical treatment to properly ground all of the observed scenarios. Expand
Complexity reduction ansatz for systems of interacting orientable agents: Beyond the Kuramoto model.
TLDR
For this generalized class of model systems, it is demonstrated that the dynamics again contain an invariant manifold, hence enabling previously inaccessible analysis and improved numerical study, allowing a similar simplified description of these systems. Expand
Coexistence of Quantized, Time Dependent, Clusters in Globally Coupled Oscillators.
We report on a novel collective state, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phaseExpand
Explosive first-order transition to synchrony in networked chaotic oscillators.
TLDR
This work demonstrates the existence of a first-order transition towards synchronization of the phases of the networked units, the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications. Expand
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