Kuramoto-Sivashinsky PDE Lyapunov Exponents: Code & Data

MATLAB 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(dx²).
• 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.