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A toolbox for finding horseshoes in 2D maps

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By Qingdu Li,
Institute for Nonlinear Systems, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China.
Email: liqd@cqupt.edu.cn or qingdu_li@163.com

As one of the most important results in chaotic dynamics, topological horseshoe theory provides a powerful tool in rigorous studies of chaos 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.

HSTOOL is a MATLAB toolbox trying to make it easy to find a horseshoe. The program is written according the method proposed in [1]. The toolbox utilizes graphical user interface. Readers only need to write an m-function for their chaotic maps (or Poincar'e maps for time-continuous system). Beside this, almost all operations for finding a horseshoe are mouse clicks, so it is user-friendly. 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. With this tool, it become very efficient to find a horseshoe in a common 2D chaotic map. For most
application, it is just a work of making several clicks with a mouse.

The current version of HSTOOL is the first 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 Xiao-Song Yang. A simple method for finding horseshoes.

Free download from Shareware Connection - As one of the most important results in chaotic dynamics, topological horseshoe theory provides a powerful tool in rigorous studies of chaos in dynamical systems, such as giving the topological entropy, verifying the existence of chaos, showing the s

Publisher: Qingdu Li | License: Shareware
Version: 1.0 | Size: 891 KB | Platform: Matlab, Scripts
Released Date: 09-06-2013 | Rating: 0 | Title: A toolbox for finding horseshoes in 2D maps

Author Url: http://www.mathworks.com
Program Info Url: http://www.mathworks.com
Download Url: http://www.mathworks.com/matlabcentral/fx_files/14075/4/hstool.zip

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