论文标题
耦合振荡器的高阶相减小
High-Order Phase Reduction for Coupled Oscillators
论文作者
论文摘要
我们探讨了耦合参数较高阶的耦合振荡器网络的相减小。对于可以明确引入相位的耦合Stuart-Landau振荡器，我们开发了一个分析性扰动程序，以明确地获得高阶近似值。我们通过得出三个Stuart-Landau振荡器网络的二阶方程来证明这一点。对于无法使用该阶段的显式表达式的系统，我们提供了一个数值过程，该过程构建了一个小型耦合单元网络的相位动力学方程。我们将这种方法应用于三个范德式振荡器的网络，并在相互作用强度的缩放范围内揭示了耦合中的组件。
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 allow for the obtaining of the higher-order approximation explicitly. 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.
