Lagrangian betweenness: a measure of bottlenecks in dynamical systems with oceanographic examples
Ser-Giacomi, E.; Baudena, A.; Rossi, M. Follows, V., Vasile, R.; Lopez, C.; Hernandez-Garcia, E.
The study of connectivity patterns in networks has brought novel insights on diverse fields ranging from neuroscience to epidemic spreading or climate. In this context, betweenness centrality has demonstrated to be a very effective measure to identify network 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 and to quantitatively relate 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. Finally, we discuss how Lagrangian betweenness could bring new insights in the network field, geophysics and fluid-dynamics.