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3D Topological Horseshoes with 1-Directional Expansion and Application in Compass Walking Model
LI Qingdu, ZHAO Wubin, YANG Fangyan
CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2016, 33 (1): 108-116.  
Abstract312)   HTML0)    PDF (1189KB)(1313)      
It is hard to apply topological horseshoe in 3D maps due to high dimension and complex structure since dimension of a chaotic attractor is often lower than its state space. We fit a surface with attractor near a selected unstable periodic orbit, and present a "dimension reduction" method to find topological horseshoes with one-directional expansion in 3D space. It is realized with a MATLAB toolbox. Compass walking model is shown to verify effectiveness, and illustrates detailed procedure for finding a topological horseshoe. It successfully verifys existence of chaotic gait and analyzes chaotic invariant set with horseshoe.
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