title: Synchronization in the random-field Kuramoto model on complex networks.
abstract: We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis, we apply the Ott-Antonsen method and the annealed-network approximation to find the critical behavior of the order parameter. In the case of homogeneous fields, we find a tricritical point above which a second-order phase transition gives place to a first-order phase transition when the network is either fully connected or scale-free with the degree exponent γ>5. Interestingly, for scale-free networks with 2<γ≤5, the phase transition is of second-order at any field magnitude, except for degree distributions with γ=3 when the transition is of infinite order at K_{c}=0 independent of the random fields. Contrary to the Ising model, even strong Gaussian random fields do not suppress the second-order phase transition in both complete graphs and scale-free networks, although the fields increase the critical coupling for γ>3. Our simulations support these analytical results.
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.|College of Engineering, Mathematics and Physical Sciences, University of Exeter, Devon EX4, United Kingdom.|Wellcome Trust Centre for Biomedical Modelling and Analysis, University of Exeter, Devon EX4, United Kingdom.|EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Devon EX4, United Kingdom.
authors: M A
authors: MA
authors: Lopes
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: E M
authors: EM
authors: Lopes
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: S
authors: S
authors: Yoon
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: J F F
authors: JF
authors: Mendes
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.|A.F. Ioffe Physico-Technical Institue, 194021 St. Petersburg, Russia.
authors: A V
authors: AV
authors: Goltsev