AI 中文总结
该研究针对时延Kuramoto模型，提出基于时延相互作用高阶近似的控制框架，运用相关方法得到序参量动力学约化方程，经数值模拟验证其比传统方法更能准确预测系统动力学，还能实现双稳和中间同步态，证明了时延高阶解释对控制振子网络的有效性。
AI 中文摘要
我们提出了一个基于时延相互作用的无延迟高阶近似来控制时延Kuramoto模型集体动力学的框架。通过将Ott--Antonsen假设和二阶平均方法应用于所得高阶Kuramoto模型，得到序参量动力学的一维约化方程。数值模拟表明，高阶近似比传统成对近似更准确地预测原延迟系统的动力学，并能实现双稳和中间同步态。结果证明了时延高阶解释对控制有时延相互作用的振子网络的有效性。
英文摘要
We propose a framework for controlling the collective dynamics of the time-delayed Kuramoto model based on a delay-free, higher-order approximation of the delayed interactions. By applying the Ott--Antonsen ansatz and the second-order averaging method to the resulting higher-order Kuramoto model, we obtain a one-dimensional reduced equation for the order parameter dynamics. Numerical simulations demonstrate that the higher-order approximation predicts the dynamics of the original delayed system more accurately than the conventional pairwise approximation and enables the realization of bistability and intermediate synchronization states. Our results demonstrate the effectiveness of higher-order interpretations of time delays for the control of oscillator networks with time-delayed interactions.
