Sarkar Mrinal, Gupta Shamik
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Department of Physics, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math, Howrah 711202, India and Quantitative Life Sciences Section, ICTP-Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.
Phys Rev E. 2020 Sep;102(3-1):032202. doi: 10.1103/PhysRevE.102.032202.
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of phase oscillators of distributed frequencies that are globally coupled through the sine of their phase differences. We study here a variation of the model by including nearest-neighbor interactions on a one-dimensional lattice. While the mean-field interaction resulting from the global coupling favors global synchrony, the nearest-neighbor interaction may have cooperative or competitive effects depending on the sign and the magnitude of the nearest-neighbor coupling. For unimodal and symmetric frequency distributions, we demonstrate that as a result, the model in the stationary state exhibits in contrast to the usual Kuramoto model both continuous and first-order transitions between synchronized and incoherent phases, with the transition lines meeting at a tricritical point. Our results are based on numerical integration of the dynamics as well as an approximate theory involving appropriate averaging of fluctuations in the stationary state.
由Kuramoto模型提供了一个用于研究自发集体同步现象的范式框架，该模型包含大量频率分布各异的相位振荡器，它们通过相位差的正弦进行全局耦合。我们在此研究该模型的一种变体，即在一维晶格上加入最近邻相互作用。虽然全局耦合产生的平均场相互作用有利于全局同步，但最近邻相互作用可能具有协同或竞争效应，这取决于最近邻耦合的符号和大小。对于单峰和对称频率分布，我们证明，结果是，该模型在稳态下与通常的Kuramoto模型形成对比，在同步相和非相干相之间呈现连续和一阶转变，且转变线在一个三临界点相交。我们的结果基于动力学的数值积分以及一个涉及稳态下涨落适当平均的近似理论。
