论文标题
具有一般相互作用强度的两个社区嘈杂的库拉莫托模型：第一部分
Two-community noisy Kuramoto model with general interaction strengths: Part I
论文作者
论文摘要
我们将在两个相互作用社区的网络中考虑的嘈杂的库拉莫托模型的研究概括为在这个情况下，将社区内部和整个社区的相互作用强度一般不同。通过开发对自洽方程的几何解释，我们能够将参数空间分离为十个区域，在该区域中，我们可以在稳态下确定最大的解决方案数量。此外，我们证明在稳态中，仅在两个群落的平均阶段之间可能只有角度0和$π$，并为非同步解决方案得出解决方案边界。最后，我们在与对称同步解决方案相对应的参数空间中识别等于类别的关系。
We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. By developing a geometric interpretation of the self-consistency equations, we are able to separate the parameter space into ten regions in which we identify the maximum number of solutions in the steady state. Furthermore, we prove that in the steady-state only the angles 0 and $π$ are possible between the average phases of the two communities and derive the solution boundary for the unsynchronized solution. Lastly, we identify the equivalence class relation in the parameter space corresponding to the symmetrically synchronized solution.
