Sharkovski ordering in a delayed perturbation of the Roessler ODE

This a program to accompany paper

Sharkovskii theorem for Delay DifferentialEquations and other infinite dimensionaldynamical systems.

by Anna Gierzkiewicz and Robert Szczelina (2024) [Preprint]

If you have the doi version of this repository, check the github [https://github.com/robsontpm/sharkovski-roessler-dde] for eventual changes.

Compilation

The project requires downloading and installing capdDDEs library: [https://github.com/robsontpm/capdDDEs]. The library itself uses CAPD [http://capd.ii.uj.edu.pl/], but it is included in the repo already.

Steps to compile and run programs:

# clone the parent repository
git close https://github.com/robsontpm/capdDDEs

# build that repository
cd capdDDEs/
bash tldr.sh

# go to the right place to store your own programs
# this will make use of the capdDDEs compilation infrastructure
cd programs/results

# clone this repository
git clone https://github.com/robsontpm/sharkovski-roessler-dde
cd sharkovski-roessler-dde

# build all programs
make all

# run the proof
cd scripts
bash RUN_PROOF.sh

NOTE: The running time is approximately 3h on ~3GHz PC with 10 availabe physical cores. If you have more cores, you can edit RUN_PROOF.sh to change NUM_JOBS=10 into NUM_JOBS=20 (if you have 20 cores).

Troubleshooting

The codes will most likely not compile on Windows.

The codes will most likely not work on Mac. hey should compile, but you might need to generate data from scratch. See below for detials.

The proof was prepared and run on Ubuntu 20.04.6 LTS, compiled with gcc (Ubuntu 9.4.0-1ubuntu1~20.04.2) 9.4.0. Any PC with x86 architecture should be able to run the proof. In a rare case, that the proof fails, it might be needed to recreate data from scratch. See README.md in scripts/ to see how to do that.

In case of any problems, do not hesitate to contact us by email: robert(dot)szczelina(at)uj(dot)edu(dot)pl.

Project structure

• bin this is where compiled programs go
• scripts this is where the protocol of the proof is established as a collection of bash/python scripts. Since proof is more involved than the version for ODEs, especially the generating the data for proofs, we decided to automate it for user convenience. We use scripting languages as they are easier to read and follow, brake down into parts that can be run separatley than a very complicated one-file-does-everything program in C++. For the sake of completeness and reproductibility, we include the full protocol described in the manuscript, so that anyone can recreate the data from scratch or use/modify it to do the proof for other interesting cases.
• proof-data data and results from the following the protocol on our computers. You can check the proof on yours computer just by doing the last step - veryfication
• proof-output here the output of the proof will be stored. For convenience, we put here the data obtained on our PC. Also, there are some gnuplot scripts to generate nice pictures used in the accompanying paper.
• tmp this directory will show up only if you are regenerating data from scratch, following the protocol in scripts.
• Makefile This guides the compilation. Its structure is such that it works if one put the repository inside the programs/results of the main ddesCAPD package.
• .h and .cpp files - the main ingredients of the computer assisted part. In header files are common subroutines, and source code files should have names describing their use. Each source file, except of utils.cpp will produce separate program in the /bin directory. See how they are used in proof-scripts
• .gitignore this is a standard git configuration file
• README.md this file, in markup format, that can be pretty-formated by various programs (github, sublime text, etc).
• TODO.md developers comments