论文标题
改进了广义库拉莫托模型的数值方案
Improved Numerical Scheme for the Generalized Kuramoto Model
论文作者
论文摘要
我们提出了一种改进，更准确的数值方案，用于将耦合相振荡器的库拉莫托模型概括为三维空间。目前的数值方案至关重要地依赖于我们的观察结果，即广义的库拉莫托模型对应于具有刚性体旋转的单位球上的颗粒，并依赖于位置依赖的角速度。我们证明，我们的改进方案能够再现已知的分析结果并捕获各种情况下三维振荡器的预期行为。另一方面，我们发现传统的数值方法与限制的直接数值集成在一起，该约束迫使粒子在每个时间步骤上都在单位球上，可能会导致不准确和误导性行为，尤其是在长时间限制下。我们详细分析了两种方法之间差异的起源，并提出了我们方法在研究库拉莫托振荡器的极限周期中的有效性。
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the generalized Kuramoto model corresponds to particles on the unit sphere undergoing rigid body rotations with position-dependent angular velocities. We demonstrate that our improved scheme is able to reproduce known analytic results and capture the expected behavior of the three-dimensional oscillators in various cases. On the other hand, we find that the conventional numerical method, which amounts to a direct numerical integration with the constraint that forces the particles to be on the unit sphere at each time step, may result in inaccurate and misleading behavior especially in the long time limit. We analyze in detail the origin of the discrepancy between the two methods and present the effectiveness of our method in studying the limit cycle of the Kuramoto oscillators.
