Extended finite-size scaling of synchronized coupled oscillators

Abstract

We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with non-identical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of phase synchronization. In particular, we extend finite-size scaling (FSS) in the steady state to dynamics, determine critical exponents, and find the critical coupling strength. The dynamic scaling approach enables us to measure not only the FSS exponent associated with the correlation volume in finite systems but also thermodynamic critical exponents. Based on the extended FSS theory, we also discuss how the sampling of natural frequencies and thermal noise affect dynamic scaling, which is numerically confirmed.

8 pages, 8 figures (18 eps files), 1 table; publised version

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• Spontaneous synchrony in power-grid networks
• Chimera States in Mechanical Oscillator Networks
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Entrainment transition in populations of random frequency oscillators
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Cited by in corpus (12)

• The Kuramoto model in complex networks
• Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs
• Transition to Collective Oscillations in Finite Kuramoto Ensembles
• Finite-Time-Finite-Size Scaling of the Kuramoto Oscillators
• Critical dynamics of the Kuramoto model on sparse random networks
• What makes us humans: Differences in the critical dynamics underlying the human and fruit-fly connectome
• Universality classes of generalized epidemic process on random networks
• Chimera states in neural networks and power systems
• Synchronization transition of the second-order Kuramoto model on lattices
• Improving power-grid systems via topological changes, or how self-organized criticality can help stability
• Modelling on the very large-scale connectome
• Natural Ordering and Uniform Tidal Effects in Globally Coupled Phase Oscillator Models