Explosive synchronization with asymmetric frequency distribution.
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 direction. We characterize two interesting coherent states in the system: In the former, two phase-locking clusters are formed, rotating with the same frequency. They correspond to those oscillators with relatively high frequencies while the oscillators with relatively small frequencies are not entrained. In the latter, two phase-locking clusters rotate with different frequencies, leading to the oscillation of the order parameter. We further conduct theoretical analysis to reveal the relation between the asymmetric frequency distribution and the conversion of synchronization type, and justify the coherent states observed in the system.
Department of Physics, East China Normal University, Shanghai, 200241, China.
Wenchang
W
Zhou
Department of Physics, East China Normal University, Shanghai, 200241, China.|Management School, The University of Sheffield, Western Bank, Sheffield S10 2TN, United Kingdom.
Lumin
L
Chen
Department of Physics, East China Normal University, Shanghai, 200241, China.
Hongjie
H
Bi
Department of Physics, East China Normal University, Shanghai, 200241, China.
Xin
X
Hu
Department of Physics, East China Normal University, Shanghai, 200241, China.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Zonghua
Z
Liu
Department of Physics, East China Normal University, Shanghai, 200241, China.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Shuguang
S
Guan
D003198:Computer Simulation; D008962:Models, Theoretical; D010507:Periodicity