论文标题
耦合相振荡器种群的通用缩放和相变
Universal scaling and phase transitions of coupled phase oscillator populations
论文作者
论文摘要
库拉莫托模型是研究振荡系统同步现象的范式，已知在宏观阶阶参数中表现出二阶，即连续的相变。在这里，我们通过在同步开始时分析捕获顺序参数的临界缩放来概述许多经典结果。使用自洽的方法并构建特征函数，我们确定了向同步的各种相变，并建立了缩放关系，描述了顺序参数对临界点附近耦合强度的渐近依赖性。我们发现，特征函数的几何特性取决于固有频率分布，它决定了订单参数的缩放属性，而不是关键性。
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize a number of classical results by presenting a general framework for capturing, analytically, the critical scaling of the order parameter at the onset of synchronization. Using a self-consistent approach and constructing a characteristic function, we identify various phase transitions toward synchrony and establish scaling relations describing the asymptotic dependence of the order parameter on coupling strength near the critical point. We find that the geometric properties of the characteristic function, which depends on the natural frequency distribution, determines the scaling properties of order parameter above the criticality.
