Finite-size scaling of synchronized oscillation on complex networks

Abstract

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P(k)\sim k^{-\gamma }$ at large $k$, we found that the finite size exponent $\bar{\nu }$ takes on the value 5/2 when $\gamma >5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu }$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytic expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations.

7 pages

References in corpus (21)

• Epidemic spreading in scale-free networks
• Resilience of the Internet to random breakdowns
• Epidemic dynamics and endemic states in complex networks
• Synchronization in small-world systems
• Universal Behavior of Load Distribution in Scale-free Networks
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Generation of uncorrelated random scale-free networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• The onset of synchronization in large networks of coupled oscillators
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Factors that predict better synchronizability on complex networks
• Frequency synchronization in random oscillator network
• Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators
• Finite-size scaling in complex networks
• Critical phenomena in networks
• Synchronization transition in scale-free networks: Clusters of synchrony
• Potts model on complex networks
• Entrainment transition in populations of random frequency oscillators
• First- and second-order phase transitions in scale-free networks
• Synchronization transition of heterogeneously coupled oscillators on scale-free networks
• Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks

Cited by in corpus (20)

• Critical phenomena in complex networks
• The Kuramoto model in complex networks
• Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks
• Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model
• Synchronization in interdependent networks
• Transition to Collective Oscillations in Finite Kuramoto Ensembles
• Nature of synchronization transitions in random networks of coupled oscillators
• Effect of time delay on the onset of synchronization of the stochastic Kuramoto model
• On the onset of synchronization of Kuramoto oscillators in scale-free networks
• Link-disorder fluctuation effects on synchronization in random networks
• Phase-shift inversion in oscillator systems with periodically switching couplings
• To synchronize or not to synchronize, that is the question: finite-size scaling and fluctuation effects in the Kuramoto model
• Thermodynamics aspects of noise-induced phase synchronization
• Finite-size scaling in globally coupled phase oscillators with a general coupling scheme
• Validity of annealed approximation in a high-dimensional system
• How to grow an oscillator network with enhanced synchronization
• Universality of critical dynamics on a complex network
• Nonlinear waves on circle networks with excitable nodes
• Noise-induced synchronization in the Kuramoto model on finite 2D lattice
• Coupled effects of local movement and global interaction on contagion