title: Synchronization of phase oscillators with frequency-weighted coupling.
abstract: Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogeneous couplings.
authors.affiliation: College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.|Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Can
authors.initials: C
authors.lastname: Xu
authors.affiliation: Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Yuting
authors.initials: Y
authors.lastname: Sun
authors.affiliation: Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Jian
authors.initials: J
authors.lastname: Gao
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Tian
authors.initials: T
authors.lastname: Qiu
authors.affiliation: College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Zheng
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Shuguang
authors.initials: S
authors.lastname: Guan