Transport in time-dependent dynamical systems: Finite-time coherent sets

2010/11/11 by Gary Froyland, Naratip Santitissadeekorn, Adam H. Monahan +1 · 12 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · doi:10.1063/1.3502450

openalex publication_date 2010/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the transport properties of nonautonomous chaotic dynamical systems over a finite-time duration. We are particularly interested in those regions that remain coherent and relatively nondispersive over finite periods of time, despite the chaotic nature of the system. We develop a novel probabilistic methodology based upon transfer operators that automatically detect maximally coherent sets. The approach is very simple to implement, requiring only singular vector computations of a matrix of transitions induced by the dynamics. We illustrate our new methodology on an idealized stratospheric flow and in two and three-dimensional analyses of European Centre for Medium Range Weather Forecasting (ECMWF) reanalysis data.

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