A toolbox for finding hyperchaotic horseshoes in hyperchaotic 3D maps

This GUI programe presents an efficient method for finding hyperchaotic topological horseshoes in hy

By Qingdu Li, Song Tang
Institute for Nonlinear Systems, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China.
Email: [e-mail], [e-mail]
2013.05.25
As one of the most important results in Hyperchaotic dynamics, topological horseshoe theory provides a powerful tool in rigorous studies of chaos and hyperchaos in dynamical systems, such as giving the topological entropy, verifying the existence of chaos, showing the structure of chaotic attractors, revealing the mechanism inside of chaotic phenomena and so on. However, this theory is not applicable for most readers because it is hard to find a topological horseshoe.
HSTOOL2.0 which trying to make it easy to find a Hyperchaotic horseshoe is a update version of HSTOOL1.0*. The program is written according the method proposed in [1]. Relative to HSTOOL1.0, the new versoin toolbox not only provides all function of HSTOOL1.0, but also is more user-friendly owing to fulfilling dynamic loading of targeted system. Instead of writting an m-function for their chaotic maps (or Poincaré maps for time-continuous system), reseachers only fill in nesscessary information of targeted system. Beside this, almost all operations for finding a horseshoe are mouse clicks, which is same to HSTOOL1.0. For example, in order to take a polygon (D_i), one first clicks the left button of the mouse on each vertex one by one, then clicks the right button to end the operation. When finding a hyperchaotic househorses, there is additionally simple step that is click the button named “ Plot Map”, the 3D houseshoes will be computed and plotted automatically. With this tool, it become very efficient to find a horseshoe in a common 2D chaotic map or a hyperchaotic horseshoe in a common 3D chaotic map. For most application, it is just a work of making several clicks with a mouse.
The current version of HSTOOL is the 2nd version. The source codes with a demo animation are available via Email to the author.
Suggestions and questions from users are most welcome for the author to update the toolbox in the future.
Reference
[1]Qingdu Li and Song Tang,[2013] “Algorithm for Finding Horseshoes in 3D Hyperchaotic Maps and Its Application” (in chinese),Acta Physica Sinnica 62, 20510.
[2] Li, Q. D. & Yang, X. S. [2010] "A Simple Method for Finding Topological Horseshoes," International Journal of Bifurcation and Chaos 20, 467-478.
* HSTOOL1.0 download: http://www.mathworks.com/matlabcentral/fileexchange/14075