Synchronization transition of heterogeneously coupled oscillators on scale-free networks

Abstract

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of $\couplingcoeff k_i^{η-1}$. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $\eta >\lambda -2$ ($\eta <\lambda -2$). We find eight different synchronization transition behaviors depending on the values of $\eta$ and $\lambda$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.

11 pages, 3 figures and two tables

References in corpus (11)

• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Global organization of metabolic fluxes in the bacterium, Escherichia coli
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Universality in the synchronization of weighted random networks
• The onset of synchronization in large networks of coupled oscillators
• Sandpile on Scale-Free Networks
• Frequency synchronization in random oscillator network
• Synchronization transition in scale-free networks: Clusters of synchrony
• Sandpile avalanche dynamics on scale-free networks
• Evolution of scale-free random graphs: Potts model formulation
• Spin Glass Phase Transition on Scale-Free Networks

Cited by in corpus (12)

• Synchronization in complex networks
• Critical phenomena in complex networks
• The Kuramoto model in complex networks
• Explosive Phenomena in Complex Networks
• Partially Locked States in Coupled Oscillators due to Inhomogeneous Coupling
• Bounding network spectra for network design
• Finite-size scaling of synchronized oscillation on complex networks
• Nature of synchronization transitions in random networks of coupled oscillators
• To synchronize or not to synchronize, that is the question: finite-size scaling and fluctuation effects in the Kuramoto model
• Transition from the self-organized to the driven dynamical clusters
• Validity of annealed approximation in a high-dimensional system
• Spectral densities of scale-free networks