MacMillan Theodore, Ouellette Nicholas T
Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, USA.
Sci Rep. 2024 Sep 5;14(1):20691. doi: 10.1038/s41598-024-71756-x.
The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier-Stokes equations in which energy "cascades" from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.
动力系统的频谱分析是分析各种系统的常用技术。但除了其分析效用外，它也是定义和解释许多物理现象的主要视角。流体力学中的湍流能量级串是三维纳维-斯托克斯方程的一个动力学结果，其中能量从大的注入尺度“级串”到较小的耗散尺度，这是一个仅在倒易空间中精确定义的著名例子。在网络动力系统背景下的相关技术在推导降阶模型方面取得了巨大成功。但这些技术在分析易处理性方面的收获，往往在可解释性和局部性方面有所损失，因为低自由度系统通常包含来自网络所有节点的信息。在这里，我们证明了一个非线性振荡器网络表现出由类似于湍流中雷诺应力的有效力促进的频谱能量转移，这是一种涌现的高阶相互作用的例子。然后，引入受大涡模拟启发的基于滤波器的分解方法，我们表明这种高阶相互作用可以定位到单个节点，并研究局部拓扑对这种相互作用的影响。
