标题： 相位还原解释了孤子形状：当多体相互作用重要时 显示英文标题

标题： Phase reduction explains chimera shape: when multi-body interaction matters

摘要： 我们提出了一种对网络中Kuramoto-Sakaguchi模型的扩展，推导出一个振荡网络的典型模型——非相同Stuart-Landau振子通过任意耦合矩阵成对耦合的二阶相位近似。 我们明确展示了该矩阵如何转化为相位方程中的耦合结构。 为了展示我们方法的强大性和高阶相位约简的关键重要性，我们处理了一个流行的非局部耦合振子设置，该设置表现出一种混沌态。 我们发现，我们的二阶相位模型能够再现混沌态形状对耦合强度的依赖关系，而通常使用的首阶Kuramoto类似模型无法捕捉到这一点。 我们的推导有助于更好地理解复杂网络的动力学，建立耦合矩阵与高阶相位模型中多体相互作用项之间的关系。 显示英文摘要

摘要： We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks - an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely via an arbitrary coupling matrix. We explicitly demonstrate how this matrix translates into the coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of non-locally coupled oscillators exhibiting a chimera state. We reveal that our second-order phase model reproduces the dependence of the chimera shape on the coupling strength that is not captured by the typically used first-order Kuramoto-like model. Our derivation contributes to a better understanding of complex networks' dynamics, establishing a relation between the coupling matrix and multi-body interaction terms in the high-order phase model.