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lyapexpts_ksperiodic.zip (253.31 kB)

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lyapexpts_ksoddperiodic.zip (255.45 kB)

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# Kuramoto-Sivashinsky PDE Lyapunov Exponents: Code & Data

dataset

posted on 2024-07-12, 01:04 authored by Russell EdsonRussell Edson, Judith Bunder, Trent MattnerTrent Mattner, Anthony RobertsAnthony RobertsMATLAB code and the generated datasets for the Lyapunov exponent spectra of the Kuramoto-Sivashinsky PDE, as published in the paper *'Lyapunov Exponents of the Kuramoto-Sivashinsky PDE'* in 2019. The files are organised as follows:

**Code**

**code/lyapunovexpts.m**contains a MATLAB function implementation of*Algorithm 1*from the paper, which is the classic algorithm for finding Lyapunov exponents introduced by Benettin et al. (1980) and Shimada and Nagashima (1979).**code/dudt_ksperiodic_spectral.m**contains a vectorised ODE-discretisation of the Kuramoto-Sivashinsky PDE on a periodic domain using a spectral scheme, which can be used with the standard MATLAB ODE solvers to simulate the dynamics.**code/dudt_ksoddperiodic_finitediff.m**contains a similar vectorised ODE-discretisation of the Kuramoto-Sivashinsky PDE, but for the "odd-periodic" domain (u = u_{xx}= 0 on x=0,L) and using a finite-difference scheme with error O(dx^{2}).**code/research_kslyaps{.m,.sh}**contain the code that ran the computational experiments (using the above Lyapunov exponents code and the Kuramoto-Sivashinsky ODE-discretisations) to generate the Lyapunov spectra data using MATLAB 2016a on the School of Mathematical Sciences' maths1 Linux server in 2017.

**Data**

**lyapexpts_ksperiodic.zip**contains the Lyapunov spectra computed for the Kuramoto-Sivashinsky PDE on the periodic domain. Each file has a filename of the form**LXYZpW.txt**, and contains the 24 most positive Lyapunov exponents computed on the periodic domain [0, L] where L = XYZ.W. (E.g., L097p4.txt contains the exponents for L=97.4.)**lyapexpts_ksoddperiodic.zip**contains the Lyapunov spectra computed for the Kuramoto-Sivashinsky PDE on the "odd-periodic" domain. Each file has a filename of the form**LXYZpW.txt**, and contains the 24 most positive Lyapunov exponents computed on the odd-periodic domain [0, L] where L=XYZ.W.

## Funding

### Complex Multiscale Systems: Modeling, Analysis and Scientific Computation

Australian Research Council

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