相位约化解释嵌合体形态：当多体相互作用起关键作用时
Phase reduction explains chimera shape: when multi-body interaction matters
AI总结：
本研究扩展Kuramoto-Sakaguchi模型，推导非全同Stuart-Landau振子网络的二阶相位近似，揭示其可捕捉一阶模型无法解释的嵌合体形态-耦合强度依赖关系，建立耦合矩阵与多体相互作用的关联。
摘要：
我们提出了网络用Kuramoto-Sakaguchi模型的扩展形式，针对一类典型振荡网络模型——由非全同Stuart-Landau振子通过任意耦合矩阵成对耦合构成的集合——推导了二阶相位近似。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。为说明我们方法的效力以及高阶相位约化的关键作用，我们研究了一类展现嵌合体状态的非局部耦合振子前沿研究场景。我们发现，我们的二阶相位模型能够复现嵌合体形态对耦合强度的依赖关系，而常用的一阶类Kuramoto模型无法捕捉这一特性。我们的推导有助于更好地理解复杂网络动力学，建立了耦合矩阵与高阶相位模型中多体相互作用项之间的关联。
英文摘要：
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.
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