The backward phase flow method for the Eulerian finite time Lyapunov exponent computations | Zendy

Shingyu Leung | Zendy

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The backward phase flow method for the Eulerian finite time Lyapunov exponent computations

Author(s) -

Shingyu Leung

Publication year - 2013

Publication title -

chaos an interdisciplinary journal of nonlinear science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.971

H-Index - 113

eISSN - 1089-7682

pISSN - 1054-1500

DOI - 10.1063/1.4847175

Subject(s) - aperiodic graph , lyapunov exponent , flow (mathematics) , computation , mathematics , exponent , eulerian path , stability (learning theory) , simple (philosophy) , control theory (sociology) , computer science , algorithm , chaotic , geometry , combinatorics , linguistics , philosophy , control (management) , epistemology , lagrangian , artificial intelligence , machine learning

We propose a simple Eulerian approach to compute the moderate to long time flow map for approximating the Lyapunov exponent of a (periodic or aperiodic) dynamical system. The idea is to generalize a recently proposed backward phase flow method which is specially designed for long time level set propagation. Unlike the original phase flow method or the backward phase flow method, which is applicable only to autonomous systems, the current approach can also be applied to any time-dependent (periodic or aperiodic) flow. We will discuss the stability of the proposed method. Numerical examples will be given to demonstrate the effectiveness of the algorithm. (C) 2013 AIP Publishing LLC

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