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Phys Rev E. 2016 Dec;94(6-1):062204. doi: 10.1103/PhysRevE.94.062204. Epub 2016 Dec 6.

Dynamics of phase oscillators with generalized frequency-weighted coupling.

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Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, P.O. Box 407, 9700 AK, The Netherlands.
Department of Physics, East China Normal University, Shanghai 200241, China.


Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.


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