2001 A four-dimensional system with a non-trivial attractor

Christophe LETELLIER

Denise Sciamarella and Gabriel Mindlin designed the four-dimensional system [1]

PNG - 16.6 ko

from a three-dimensional system proposed by Deng [2] For appropriate parameter values as

PNG - 4.7 ko

this system produces a chaotic attractor (Fig. 1). A solution to this system was investigated with a cell complex in their work. It was recently revisited in terms of templex [3]

JPG - 39.1 ko
Fig. 1. Chaotic attractor produced by the four-dimensional system.

From the complex of cells Here, a templex was built and, then, a template constructed as drawn in Fig. 2.

JPG - 34 ko
Fig. 2. A direct template for the four-dimensional attractor.
Zip - 1.1 ko
A C++ code for integrating the 4-dimensional system.

[1] D. Sciamarella & G. B. Mindlin, Unveiling the topological structure of chaotic flows from data, Physical Review E, 64, 036209, 2001.

[2] B. Deng, Constructing homoclinic orbits and chaotic attractors, International Journal of Bifurcation & Chaos, 4, 823-841, 1994.

[3] G. D. Charó, C. Letellier & D. Sciamarella, Templex : A bridge between homologies and templates for chaotic attractors, Chaos, 32 (8), 083108, 2022. Online


A C++ code for integrating the 4-dimensional system.
Zip · 1.1 ko
8874 - 21/06/24

Fatal error: Cannot redeclare boucle_date_edithtml_733e07738d6277dcad4536fa7a13561b() (previously declared in /htdocs/public/www/ecrire/public/composer.php(48) : eval()'d code:11) in /htdocs/public/www/ecrire/public/composer.php(48) : eval()'d code on line 161