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 $\gamma >5$. Interestingly, for scale-free networks with $2<\gamma \le 5$, the phase transition is of second-order at any field magnitude, except for degree distributions with $\gamma =3$ when the transition is of infinite order at $K_c=0$ independently on the random fields. Contrarily 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 though the fields increase the critical coupling for $\gamma >3$. Our simulations support these analytical results.

7 pages, 2 figures

References in corpus (6)

• Critical phenomena in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Explosive Synchronization Transitions in Scale-free Networks
• Kuramoto model with frequency-degree correlations on complex networks
• Evolution of scale-free random graphs: Potts model formulation
• Random field Ising model on networks with inhomogeneous connections

Cited by in corpus (6)

• Explosive Phenomena in Complex Networks
• Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
• Synchronization of Kuramoto Oscillators in Dense Networks
• Distinct dynamical behavior in Erdős-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks
• On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization
• On the Critical Coupling of the Finite Kuramoto Model on Dense Networks