Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories (Communications in Computational Physics, 2019)
We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangianparticle trajectories. The method first reconstructs the flow field using the radial basisfunction (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based onthe Schur complement for updating, rather than recomputing, the reconstruction inthe RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous andaperiodic flows, and also measurements from real-life data.
Keywords: Dynamical system; visualization; finite time Lyapunov exponent; numerical methods for differential equations.