Chulho Choi, Meesoon Ha, Byungnam Kahng
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. This provides another comprehensive view of phase synchronization in the Kuramoto model. We show how to extend the finite- size scaling (FSS) in the steady state to dynamics, and determine critical exponents and 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 the thermodynamic critical exponents. Based on the extended FSS theory, we discuss how the sampling of natural frequencies and thermal noise affect the universality of dynamic scaling according to the network topology of oscillators, which is numerically confirmed.
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http://arxiv.org/abs/1307.2408
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