具有附加最近邻相互作用的Kuramoto模型：非平衡三临界点的存在性
Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point
摘要：
仓本模型是研究自发集体同步现象的一个范例框架，它包括大量分布频率的极限环振荡器，这些振荡器通过它们的相位差的正弦全局耦合。我们在这里研究的模型的变化，包括最近邻相互作用的一维晶格。虽然由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合作或竞争效应，这取决于最近邻耦合的符号和大小。对于单峰和对称的频率分布，我们证明，作为结果，在稳态模型表现出在对比通常的仓本模型的同步和非相干相位之间的连续和一阶过渡，过渡线满足在一个三临界点。我们的研究结果是基于数值积分的动态以及一个近似的理论，涉及适当的平均波动的稳定状态。
英文摘要：
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.
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