Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model

Data and software

Paweł Pilarczyk

This website contains the data and software described in the paper Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model by D. Falęcki, M. Rosman, M. Palczewski, P. Pilarczyk, and A. Bartłomiejczyk. A preprint of the paper is available from arXiv .

Continuation diagram

There is one continuation diagram available for browsing. Please, click the small diagram below to launch an interactive browser.

The analysis was conducted for the Andrecut-Kauffman model defined by Equation (1) in the paper. The continuation diagram is explained in the preprint of the paper in Section 3.4 and is shown in Figure 4 there.

The continuation diagram shows α1 in the horizontal axis, and α2 in the vertical axis.

The Conley-Morse diagram is shown in the numeric text format described in the detail in another paper: P. Pilarczyk, J. Signerska-Rynkowska, and G. Graff, Topological-numerical analysis of a two-dimensional discrete neuron model, Chaos 33 (2023), 043110. DOI: 10.1063/5.0129859. Preprint: arXiv:2209.03443.

The phase space shows x in the horizontal axis, and y in the vertical axis, with a color bar at the bottom.

You are welcome to browse the numerical Morse decompositions and the Conley-Morse diagrams to discover the information obtaind about the dynamics using this method.

Data files used for the browser are provided in the following three zipped files:

  • gen2d11php.zip – PHP code files and PNG images for the browser provided with the source code (see below),
  • gen2d11c.zip – the Conley-Morse graphs encoded in the text format compatible with the dot program from the Graphviz Graph Visualization Software package (https://graphviz.org/),
  • gen2d11p.zip – the computed Morse decompositions encoded in terms of PNG images in which a single pixel corresponds to a square in the phase space.

(Note: if your browser doesn't download some of the data files, the reason might be that you are browsing the current page using the secure https protocol, while the files are available through the insecure http protocol. A solution to the problem might be to switch to the http protocol by editing the address in your browser's address bar and replacing "https:" with "http:", that is, deleting the letter 's'.)

Software

The computations were conducted using the Conley-Morse Graphs software configured for the Andrecut-Kauffman model. The original software was published with the first paper about the database approach to cataloging dynamics in 2009, and updated afterwards. The source code of the software that was actually used for the computations is available below for the benefit of the academic community. It is expected that those who are interested in doing similar computations for different systems or to verify our computations may benefit from this software.

This software is written in C++ and its compilation requires the CAPD software library, version 4.2.153 (the limited version "capdDynSys" is sufficient), and the Original CHomP library, as well as several other standard software libraries: boost, zlib, libpng, libbz2, and LAPACK. A relatively recent GNU C++ compiler is also necessary. Specific instructions for downloading and compiling the software in Ubuntu GNU/Linux 20.04 are provided here.