Lagrangian betweenness as a measure of bottlenecks in dynamical systems with oceanographic examples

TL;DR

This paper introduces Lagrangian betweenness, a new trajectory-based measure derived from Lyapunov exponents, to identify bottlenecks in dynamical systems like ocean circulation, with applications in ecology and fluid transport.

Contribution

It extends betweenness centrality to dynamical systems using a novel Lyapunov exponent-based formulation, linking network bottlenecks to hyperbolic points in flows.

Findings

Bottlenecks are persistent in oceanic circulation across scales.

Lagrangian betweenness correlates with ecological diversity in plankton data.

Identifies key regions influencing fluid transport in oceans.

Abstract

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.