Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories

Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories

Year:    2019

Author:    Yu-Keung Ng, Shingyu Leung

Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 1143–1177

Abstract

We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangian particle trajectories. The method first reconstructs the flow field using the radial basis function (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based on the Schur complement for updating, rather than recomputing, the reconstruction in the RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous and aperiodic flows, and also measurements from real-life data.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0149

Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 1143–1177

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    Dynamical system visualization finite time Lyapunov exponent numerical methods for differential equations.

Author Details

Yu-Keung Ng

Shingyu Leung

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