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Computing Lyapunov exponents based on the solution expression of the variational system

Computing Lyapunov exponents based on the solution expression of the variational system
Computing Lyapunov exponents based on the solution expression of the variational system
A simple discrete QR algorithm based on a solution expression of the variational equation of a dynamical system is presented for computing the Lyapunov exponents of n-dimensional continuous dynamical systems. The developed numerical scheme of study is based on a time integration using a constant time-step fourth-order Adams–Bashforth method. Numerical results are presented for a Lorenz system with known Lyapunov exponents, and higher dimensional dynamical systems. The algorithm proposed to compute the Lyapunov exponents is found to be robust, computationally efficient, and stable for a sufficiently small step-size h.
numerical computation, chaos, dynamical systems
0096-3003
982-996
Chen, Z.-M.
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Chen, Z.-M.
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c

Chen, Z.-M., Djidjeli, K. and Price, W.G. (2006) Computing Lyapunov exponents based on the solution expression of the variational system. Applied Mathematics and Computation, 174 (2), 982-996. (doi:10.1016/j.amc.2005.05.016).

Record type: Article

Abstract

A simple discrete QR algorithm based on a solution expression of the variational equation of a dynamical system is presented for computing the Lyapunov exponents of n-dimensional continuous dynamical systems. The developed numerical scheme of study is based on a time integration using a constant time-step fourth-order Adams–Bashforth method. Numerical results are presented for a Lorenz system with known Lyapunov exponents, and higher dimensional dynamical systems. The algorithm proposed to compute the Lyapunov exponents is found to be robust, computationally efficient, and stable for a sufficiently small step-size h.

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More information

Published date: 2006
Keywords: numerical computation, chaos, dynamical systems

Identifiers

Local EPrints ID: 23344
URI: https://eprints.soton.ac.uk/id/eprint/23344
ISSN: 0096-3003
PURE UUID: b77243b4-fa08-48be-8443-71feb9c6d5b4

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Date deposited: 10 Mar 2006
Last modified: 17 Jul 2017 16:17

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