Databases for the Global Dynamics of Multiparameter Systems

This website contains supplementary data for the paper Databases for the Global Dynamics of Multiparameter Systems by Zin Arai, William Kalies, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka, and Paweł Pilarczyk.

Database for the Leslie Model with p = 0.7

Phenotype classes are indicated in different colors.

Parameter boxes (indicated in red) for which there exists at least one Morse set whose Conley index was not computed because of lack of isolation.

Click each parameter box to see the corresponding Conley-Morse graph and the Morse decomposition. Note: Due to differences between browsers, the coordinates indicated in the tooltip my sometimes differ from the corresponding parameter box.

Database for the Leslie Model with All Three Varying Parameters

An animation of 40 slices of the 3D picture of phenotype classes. (Hover mouse to pause the animation, click to browse Conley-Morse graphs.)

A continuation graph automatically generated from the result of computations (Click to see a full-size PDF file.)

The palette of colors assigned to nontrivial phenotype classes oredered by the number of boxes in the class. (Click to see a description of the class.)

Note: The Conley index of the origin has been set to what follows from the analytical computations if it couldn't be computed automatically (no isolation detected), unless a bifurcation takes place for the range of parameters covered by the box.

Software for Computing Conley-Morse Graphs

Efficient software for computing Conley-Morse graphs in a distributed way in a multi-computer environment which was used to construct the above-mentioned databases can be downloaded free of charge from its author's website The software is written in C++ and its source code is available under the terms of GNU General Public License. This code can be compiled by the GNU C++ compiler in both Windows and Linux (a makefile is included). Detailed documentation generated by Doxygen is also provided.

Files for Offline Browsing

This website can be copied for offline use by downloading the compressed files listed below. Please, do not attempt to mirror this website using HTTrack or similar programs, because it contains hundreds of thousands of pages automatically generated by just a few PHP scripts, and at least twice that many pictures which are unzipped and rescaled on-the-fly. Browsing an offline copy of this website available below requires the following software:

The files that can be download are as follows: Note: some browsers don't allow downloading the zip files if the current page is viewed using the secure (https) protocol. If you encounter this problem, correct the address in your browser's address bar to add http:// at the beginning (instead of the usual https://).
The file should be unpacked into an empty directory, and the remaining files should be copied into a subdirectory called "zipped" of the directory into which has been unzipped (these files should not be decompressed).