Details

Autor(en) / Beteiligte

• Coletta, Tommaso
• Delabays, Robin
• Jacquod, Philippe

Titel

Finite-size scaling in the Kuramoto model

Ist Teil von

• Physical review. E, 2017-04, Vol.95 (4-1), p.042207-042207, Article 042207

Ort / Verlag

United States

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We investigate the scaling properties of the order parameter and the largest nonvanishing Lyapunov exponent for the fully locked state in the Kuramoto model with a finite number N of oscillators. We show that, for any finite value of N, both quantities scale as (K-K_{L})^{1/2} with the coupling strength K sufficiently close to the locking threshold K_{L}. We confirm numerically these predictions for oscillator frequencies evenly spaced in the interval [-1,1] and additionally find that the coupling range δK over which this scaling is valid shrinks like δK∼N^{-α} with α≈1.5 as N→∞. Away from this interval, the order parameter exhibits the infinite-N behavior r-r_{L}∼(K-K_{L})^{2/3} proposed by Pazó [Phys. Rev. E 72, 046211 (2005)]PLEEE81539-375510.1103/PhysRevE.72.046211. We argue that the crossover between the two behaviors occurs because at the locking threshold, the upper bound of the continuous part of the spectrum of the fully locked state approaches zero as N increases. Our results clarify the convergence to the N→∞ limit in the Kuramoto model.