3D Topological Horseshoes with 1-Directional Expansion and Application in Compass Walking Model

Abstract

Abstract: 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.

Key words: topological horseshoe, chaos, passive-walking, Compass walking model

CLC Number:

LI Qingdu, ZHAO Wubin, YANG Fangyan. 3D Topological Horseshoes with 1-Directional Expansion and Application in Compass Walking Model[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(1): 108-116.

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