Files for the numerical results shown in "Far-from-equilibrium travelling pulses in sloped semi-arid environments driven by autotoxicity effects" by Gabriele Grifò, Annalisa Iuorio, and Frits Veerman

This folder contains the code used to produce Fig. 1 and Fig. 8-10 in the paper: "Far-from-equilibrium travelling pulses in sloped semi-arid environments driven by autotoxicity effects" by Gabriele Grifò, Annalisa Iuorio, and Frits Veerman. The preprint version of this paper is available at https://arxiv.org/abs/2405.1560.

In the subfolder "Direct_simulations", the code (to obtain Fig. 1) is based on a MATLAB routine which uses finite differences for spatial discretization with periodic boundary conditions together with MATLAB’s ode15s routine for time integration.

The continuation procedure (to obtain Fig. 8-10) is shown in the subfolder "Continuation" based on the software AUTO to analyse the dependence of the constructed travelling pulse solutions of Eq. (3.2) with respect to three system parameters, i.e. A, D, and H. Correspondingly, in each folder 'Continuation_X' where X=A, D, H, the results can be obtained by running the file 'AUTO_script_cont_X', based on the two files 'parab_X.f90' and 'c.parab_X'.

Selected solutions for each continuation are stored in the corresponding subfolders 'solutions_X', whereas the tables resulting from the continuation procedure in the scripts are shown in the files 'bifdiag_X.dat'. In each script file further details are provided in order to clarify how to extract the solutions used for the plots.