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

Enrico Ser-Giacomi (), Alberto Baudena, Vincent Rossi, Mick Follows, Sophie Clayton, Ruggero Vasile, Cristóbal López and Emilio Hernández-García
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Enrico Ser-Giacomi: Massachusetts Institute of Technology
Alberto Baudena: Sorbonne Université,CNRS, Laboratoire d’Océanographie de Villefranche, UMR 7093 LOV, Villefranche‑sur‑Mer, France
Vincent Rossi: CNRS, Aix Marseille Univ., Univ. Toulon, IRD
Mick Follows: Massachusetts Institute of Technology
Sophie Clayton: Old Dominion University
Ruggero Vasile: UP Transfer GmbH
Cristóbal López: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos
Emilio Hernández-García: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos

Nature Communications, 2021, vol. 12, issue 1, 1-14

Abstract: 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.

Date: 2021
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DOI: 10.1038/s41467-021-25155-9

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