拉格朗日介数作为动力系统瓶颈的度量及海洋学实例
Lagrangian betweenness as a measure of bottlenecks in dynamical systems with oceanographic examples
摘要：
对网络中连接模式的研究为从神经科学到传染病传播或气候等不同领域带来了新的见解。在这种情况下，介数中心性已被证明是一个非常有效的措施，以确定节点作为拥塞的焦点，或瓶颈，在网络中。然而，没有一种方法可以在网络框架之外定义介数。通过分析连接动力系统和网络理论，我们提供了一个基于概率的介数，称为拉格朗日介数，作为李雅普诺夫指数的函数制定。这将介数的概念扩展到了网络理论的范围之外，将任何动力系统中的双曲点和异宿连接与与其相关的网络的结构瓶颈联系起来。使用建模和观测速度场，我们表明，这种瓶颈是存在的，令人惊讶的是，在不同的空间海洋环流持久-时间尺度，我们说明了这些地区的作用，在推动流体输送在广阔的海洋区域。通过对太平洋黑潮区浮游生物丰度数据的分析，发现多样性和介数指标之间存在显著的空间相关性，这为生态学应用提供了依据。
英文摘要：
The study of connectivity patterns in networks has brought novel insights across diverse fields ranging from neurosciences to epidemic spreading or climate. In this context, betweenness centrality has demonstrated to be a very effective measure to identify nodes that act as focus of congestion, or bottlenecks, in the network. However, there is not a way to define betweenness outside the network framework. By analytically linking dynamical systems and network theory, we provide a trajectory-based formulation of betweenness, called Lagrangian betweenness, as a function of Lyapunov exponents. This extends the concept of betweenness beyond the context of network theory relating hyperbolic points and heteroclinic connections in any dynamical system to the structural bottlenecks of the network associated with it. Using modeled and observational velocity fields, we show that such bottlenecks are present and surprisingly persistent in the oceanic circulation across different spatio-temporal scales and we illustrate the role of these areas in driving fluid transport over vast oceanic regions. Analyzing plankton abundance data from the Kuroshio region of the Pacific Ocean, we find significant spatial correlations between measures of diversity and betweenness, suggesting promise for ecological applications.
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