Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies |
| |
Authors: | Anandamohan Ghosh Shamik Gupta |
| |
Institution: | 1. Indian Institute of Science Education and Research-Kolkata, Mohanpur 741252, India;2. Laboratoire de Physique Théorique et Modèles Statistiques, UMR 8626, Université Paris-Sud 11 and CNRS, Bâtiment 100, Orsay F-91405, France |
| |
Abstract: | 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. |
| |
Keywords: | Synchronization Kuramoto model Relaxation dynamics |
本文献已被 ScienceDirect 等数据库收录! |
|