High-order phase reduction for coupled oscillators
High-order phase reduction for coupled oscillators
复制标题
DOI：
10.1088/2632-072x/abbed2
复制
发表时间：
2021-06-01
影响因子：
2.7
通讯作者：
Pikovsky, Arkady
中科院分区：
文献类型：
--
作者：
Gengel, Erik;Teichmann, Erik;Pikovsky, Arkady
我们探索了耦合参数高阶耦合振荡器网络中的相位减少。对于耦合的 Stuart-Landau 振荡器，可以明确地引入相位，我们开发了一种分析扰动程序来明确地获得高阶近似。我们通过推导三个 Stuart-Landau 振荡器网络的二阶相位方程来证明这一点。对于无法获得明确的相位表达式的系统，我们提出了一种数值程序，可以为耦合单元的小型网络构造相位动力学方程。我们将这种方法应用于三个范德波尔振荡器的网络，并揭示了耦合中相互作用强度不同比例的分量。
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation procedure to explicitly obtain the higher-order approximation. We demonstrate this by deriving the second-order phase equations for a network of three Stuart-Landau oscillators. For systems where explicit expressions of the phase are not available, we present a numerical procedure that constructs the phase dynamics equations for a small network of coupled units. We apply this approach to a network of three van der Pol oscillators and reveal components in the coupling with different scaling in the interaction strength.