TY - JOUR
T1 - Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories
AU - Ng , Yu-Keung
AU - Leung , Shingyu
JO - Communications in Computational Physics
VL - 4
SP - 1143
EP - 1177
PY - 2019
DA - 2019/07
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0149
UR - https://global-sci.org/intro/article_detail/cicp/13232.html
KW - Dynamical system, visualization, finite time Lyapunov exponent, numerical methods
for differential equations.
AB - <p style="text-align: justify;">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.</p>