论文标题
OTT-ANTONSEN方案中耦合振荡器的顺序参数动力学的研究用于通用频率分布
The study of the dynamics of the order parameter of coupled oscillators in the Ott-Antonsen scheme for generic frequency distributions
论文作者
论文摘要
Ott-Antonsen Ansatz表明，对于$ N $全球耦合的库拉莫托振荡器系统中固有频率的某些分布，订单参数的动力学，在限制$ n \ in \ infty $中，在适当的初始条件下，在低端的适当初始条件下演变。当频率分布在复杂平面中持续具有无限的基本奇异性时，这是不可能的。例如，高斯分布就是这种情况。在这项工作中，我们提出了一个简单的近似方案，该方案还允许在低维歧管中延伸到这种情况下的订单参数动力学的表示。使用作为工作示例，高斯频率分布，我们将振荡器系统的顺序参数的动力学演变与通过$ n $运动方程的数值集成获得的振荡器系统的动力学演变与在近似方案的应用中获得的低维歧管中的类似动力学。结果证实了近似值的有效性。该方法可以用于一般频率分布，从而确定振荡器系统的相应相图。
The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of $N$ globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit $N\to \infty$, evolves, under suitable initial conditions, in a manifold of low dimension. This is not possible when the frequency distribution, continued in the complex plane, has an essential singularity at infinite; this is the case for example, of a Gaussian distribution. In this work we propose a simple approximation scheme that allows to extend also to this case the representation of the dynamics of the order parameter in a low dimensional manifold. Using as a working example the Gaussian frequency distribution, we compare the dynamical evolution of the order parameter of the system of oscillators, obtained by the numerical integration of the $N$ equations of motion, with the analogous dynamics in the low dimensional manifold obtained with the application of the approximation scheme. The results confirm the validity of the approximation. The method could be employed for general frequency distributions, allowing the determination of the corresponding phase diagram of the oscillator system.
