Synchronization of phase oscillators in the generalized Sakaguchi-Kuramoto model

¹ School of Physics and Electronic Engineering, Jiangsu Normal University - Xuzhou 221116, China
² Department of Physics, Beijing Normal University - Beijing 100875, China
³ Institute of Systems Science and College of Information Science and Engineering, Huaqiao University Xiamen 361021, China

^(a) xucan@mail.bnu.edu.cn (corresponding author)
^(b) lvhp@jsnu.edu.cn (corresponding author)

Received: 7 June 2017
Accepted: 30 July 2017

Abstract

We study the synchronization transition in the frequency-weighted Kuramoto model by considering the phase shift coupling scheme. Both the macroscopic and microscopic dynamical features are characterized in the system. We identify different asymptotic coherent states for the long-term evolution of the system and reveal various phase transitions among them. Theoretically, the self-consistency approach is developed to get analytical insights, the critical coupling strength for the onset of synchronization and the effective average frequencies of oscillators can be obtained. Furthermore, the important dynamical characteristic (plateau effect) of the nonstationary state is explained which was found numerically in the paper by Bi H. et al., Phys. Rev. Lett., 117 (2016) 204101. Physically, the plateau effect essentially arises from the periodic behavior of the mean field. 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.