On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems

Authors:
Luca Dieci;Robert D. Russell;Erik S. Van Vleck
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1997

Citing 0
Cited 10

Computation of Lyapunov characteristic exponents for continuous dynamical systems

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
A numerical method for the computation of the Lyapunov exponents of nonlinear ordinary differential equations

Applied Mathematics and Computation
Computation of few Lyapunov exponents by geodesic based algorithms

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
A class of orthogonal integrators for stochastic differential equations

Journal of Computational and Applied Mathematics
Hybrid solvers for composition and splitting methods

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Computation of a few Lyapunov exponents for continuous and discrete dynamical systems

Applied Numerical Mathematics
Preserving poisson structure and orthogonality in numerical integration of differential equations

Computers & Mathematics with Applications
A class of orthogonal integrators for stochastic differential equations

Journal of Computational and Applied Mathematics
Hybrid solvers for composition and splitting methods

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
QR methods and error analysis for computing Lyapunov and Sacker---Sell spectral intervals for linear differential-algebraic equations

Advances in Computational Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, we consider discrete and continuous QR algorithms for computing all of the Lyapunov exponents of a regular dynamical system. We begin by reviewing theoretical results for regular systems and present general perturbation results for Lyapunov exponents. We then present the algorithms, give an error analysis of them, and describe their implementation. Finally, we give several numerical examples and some conclusions.