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An Improved Method for Lyapunov Exponents Computation
Authors

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
Nasri Zakia
Organization: National Institute of Applied Sciences and Technology
Department: Chemical Engineering Department
Revision date

2008-03-09
Description

We apply a modified version of the two methods descibed by M. Sandri in order to determine the maximum Lyapunov exponent and all Lyapunov exponents. The modification consisted in using NDSolve instead of the fixed step size method of Roman Maeder entitled RKStep. This allows us to get more accurate results while substantially reducing computation times. Lyapunov exponents found with our method agreed well with those obtained using the Matlab code by V.N. Govorukhin. The non-linear dynamic examples studied here are the Lorenz and the Rosler systems as well as the non-isothermal chemical system of Tomlin and Scott.

References:

[1] Sandri, M. "Numerical Calculation of Lyapunov Exponents." Mathematica J. 6, 78-84, 1996. http://library.wolfram.com/infocenter/Articles/2902

[2] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D, Vol. 16, pp. 285-317, 1985.

[3] Govorukhin V. N., MATDS is a MATLAB-based program for dynamical system investigation. It works with version 6.5 of MATLAB. http://kvm.math.rsu.ru/matds
Subjects

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering
*Mathematics > Calculus and Analysis > Dynamical Systems
*Science > Chemistry
Keywords

non-isothermal chemical system, Lyapounov exponent, chaotic behaviour, periodic behaviour, Matlab, Mathematica, Lorenz system, Rosler system, non-linear dynamics, NDSolve, GramSchmidt
Related items

*Numerical Calculation of Lyapunov Exponents   [in Articles]
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ImpLORENTZ.nb (83.7 KB) - Mathematica Notebook [for Mathematica 6.0]
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ImpNonIsothermalLyapunov.nb (468.5 KB) - Mathematica Notebook [for Mathematica 6.0]
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ImpROSLER.nb (251.7 KB) - Mathematica Notebook [for Mathematica 6.0]