Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors

Details Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors

2008-07-01

arxiv.org/abs/0807.0239v1

Mathematics

Dynamical Systems

pdflatex; 38 pages with 18 figures

Scientific paper

Finite-time Lyapunov exponents and vectors are used to define and diagnose boundary-layer type, two-timescale behavior and to construct a method for determining an associated slow manifold when one exists. Two-timescale behavior is characterized by a slow-fast splitting of the tangent bundle for the state-space. The slow-fast splitting defined by finite-time Lyapunov exponents and vectors is interpreted in relation to the asymptotic theory of partially hyperbolic sets. The method of determining a slow manifold developed in this paper is potentially more accurate than an existing approach that is based on local eigenvalues and eigenvectors, at the expense of more computation, and is more generally applicable than approaches, such as the singular perturbation method, that require a special coordinate representation. The approach is illustrated via several examples.

Affiliated with

Also associated with

No associations

Rating

Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421532