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
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
2006
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), .
(doi:10.1016/j.amc.2005.05.016).
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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Published date: 2006
Keywords:
numerical computation, chaos, dynamical systems
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Local EPrints ID: 23344
URI: http://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: 15 Mar 2024 06:46
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Author:
Z.-M. Chen
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