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Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies
The Kuramoto model describes a system of globally coupled phase-only
oscillators with distributed natural frequencies. The model in the steady state
exhibits a phase transition as a function of the coupling strength, between a
low-coupling incoherent phase in which the oscillators oscillate independently
and a high-coupling synchronized phase. Here, we consider a uniform
distribution for the natural frequencies, for which the phase transition is
known to be of first order. We study how the system close to the phase
transition in the supercritical regime relaxes in time to the steady state
while starting from an initial incoherent state. In this case, numerical
simulations of finite systems have demonstrated that the relaxation occurs as a
step-like jump in the order parameter from the initial to the final steady
state value, hinting at the existence of metastable states. We provide
numerical evidence to suggest that the observed metastability is a finite-size
effect, becoming an increasingly rare event with increasing system size.Comment: 4 pages, 5 figures; v2: 12 pages, 9 figures, published versio