论文标题
混合同步转变的有效潜在方法
Effective potential approach to hybrid synchronization transitions
论文作者
论文摘要
Kuramoto模型根据固有频率分布的类型表现出不同类型的同步转变。为了获得这些结果，已成功使用了库拉莫托自符际方程（SCE）方法。但是，这种方法仅对更详细的属性（例如稳定性和有限尺寸效应）提供了有限的理解。在这里，我们通过引入有效的潜力，即SCE的积分版本来扩展SCE方法。我们检查了在热力学极限下的二阶，一阶和杂化同步转变的有效潜力的景观。特别是，对于混合过渡，我们发现，最小有效电位显示了阶段参数跳跃的区域的平稳。该结果表明，有效的自由能可用于确定一种同步转变。对于有限系统，有效潜力包含可以将系统捕获的局部最小值。使用数值模拟，我们确定系统的稳定性是系统大小和仿真时间的函数。
The Kuramoto model exhibits different types of synchronization transitions depending on the type of natural frequency distribution. To obtain these results, the Kuramoto self-consistency equation (SCE) approach has been used successfully. However, this approach affords only limited understanding of more detailed properties such as the stability and finite size effect. Here, we extend the SCE approach by introducing an effective potential, that is, an integral version of the SCE. We examine the landscape of this effective potential for second-order, first-order, and hybrid synchronization transitions in the thermodynamic limit. In particular, for the hybrid transition, we find that the minimum of effective potential displays a plateau across the region in which the order parameter jumps. This result suggests that the effective free energy can be used to determine a type of synchronization transition. For finite systems, the effective potential contains local minima at which the system can be trapped. Using numerical simulations, we determine the stability of the system as a function of system size and simulation time.
