论文标题
具有其他最近邻次相互作用的Kuramoto模型：存在非平衡三智度点
Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point
论文作者
论文摘要
一个范式研究自发集体同步现象的范式框架是由库拉莫托模型提供的，该模型包括大量分布式频率的极限周期振荡器，这些频率通过其相位差异的正弦耦合。我们在这里研究模型的变化，通过在一维晶格上包括最近的邻居相互作用。尽管全球耦合产生的平均场相互作用有利于全球同步，但最近的邻居相互作用可能会取决于最近邻居辅助的符号和幅度。对于单峰和对称频率分布，我们证明，结果，固定态的模型与同步和不相互分相之间的常规库拉莫托模型相反，而过渡线在三个智力点相交。我们的结果基于动力学的数值整合以及涉及固定状态波动的适当平均的近似理论。
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle 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.
