An installation instruction of the program realizing computer assisted proof of the coexistence of chaotic and hyperchaotic invariant sets and heteroclinic connections between them in the 4D Rössler system.

Daniel Wilczak, Sergio Serrano and Roberto Barrio
"Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: a Computer-assisted proof"

Requirements:

The program is written in C++11. We recommend to compile and execute the program on a linux-like computer with many cores (16 at least) and not less than 32GB of memory. The program uses the CAPD library (see also sourceforge download zone) which provides in particular routines for computation of Poincare maps and their derivatives. The program has been tested with the version capd-4.2.89 which is provided in this archive for user convenience.

Compilation of the CAPD library on a linux-like system

Note: This step is optional if you have already installed the CAPD library.

Compilation of the CAPD library consist of the following steps

  1. unzip the archive
    tar xvfz capd.tar.gz
  2. enter the directory of the library
    cd capd
  3. configure the library
    ./configure --without-gui --without-boost --without-mpfr
  4. compile the library
    make lib -j

Compilation of the program

  1. In the directory program invoke
    make CAPD=relative_or_absolute_path_to_capd_bin_directory
    for example
    make CAPD=../capd/bin/
    Warning: Do not forget the last slash character.
    If the CAPD library is installed in standard directories which are on the system path (like /usr/bin/) then you can compile the program just by invoking
    make

Program execution

The prorgam can be run from the terminal by
./main
Since the computations are time consumming we recommend to redirect the standard output to a log file.
./main > log&

The program executes in a text mode. Therefore we recommend to compile and run the program on a multicore, perhaps remote computer.

Output:

The program executes within more than four hours on a computer with 64 cores using circa 30GB of memory. During the execution the program writes to the standard output information about what is being computed and if this condition is validated or not. The program writes enclosure of forward invariant set to a file located in out directory. It is about 500MB large.

Algorithms:

The algorithms are quite well (we hope) commented in the code. Please send any queries concerning the code to wilczak@ii.uj.edu.pl.