Explosive synchronization with asymmetric frequency distribution.

@article{Zhou2015ExplosiveSW,
  title={Explosive synchronization with asymmetric frequency distribution.},
  author={Wenchang Zhou and Lumin Chen and Hongjie Bi and Xin Hu and Zonghua Liu and Shuguang Guan},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={92 1},
  pages={
          012812
        }
}
In this work, we study the synchronization in a generalized Kuramoto model with frequency-weighted coupling. In particular, we focus on the situations in which the frequency distributions of oscillators are asymmetric. For typical unimodal frequency distributions, such as Lorentzian, Gaussian, triangle, and even special Rayleigh, we find that the synchronization transition in the model generally converts from the first order to the second order as the central frequency shifts toward positive… 
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References

SHOWING 1-10 OF 40 REFERENCES
Exact solution for first-order synchronization transition in a generalized Kuramoto model
TLDR
The analytical solution of a generalized Kuramoto model is reported, and a series of exact results for the first-order synchronization transition are derived, including the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions.
Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators.
TLDR
This paper simulates the Kuramoto model on top of a family of networks with different degree-degree and frequency-frequency correlation patterns and shows that only when the degrees and natural frequencies of the network's nodes are both disassortative can an explosive synchronization occur.
Kuramoto model with frequency-degree correlations on complex networks
We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical…
Explosive synchronization enhanced by time-delayed coupling.
  • T. Peron, F. Rodrigues
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
This paper deals with the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are…
Disorder induces explosive synchronization.
TLDR
It is shown that explosive synchronization can be induced in mildly heterogeneous networks by the addition of quenched disorder to the oscillators' frequencies, demonstrating that it is not only robust to, but moreover promoted by, this natural mechanism.
Explosive transitions to synchronization in networks of phase oscillators
TLDR
This work sets conditions for the transition from unsynchronized to synchronized states to be first-order, and demonstrates how these conditions can be attained in a very wide spectrum of situations.
Explosive synchronization transitions in complex neural networks.
TLDR
It is shown that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system.
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations.
  • T. Peron, F. Rodrigues
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
TLDR
It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree, which differs from those whose frequency distributions are unimodal and even.
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.
...
1
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