科研之友
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摘要
We propose a simple but effective visualization method for detecting the stretch-and-fold mechanism in chaotic dynamical systems. In the proposed method, we first place a hypersphere that is centered at a point on the trajectory of an attractor produced from the chaotic dynamical system. Second, we uniformly arrange points on the surface of the hypersphere. Third, we evolve the dynamics and observe the temporal evolution of the center point and the points on the surface. We then calculate the temporal evolution of the distances between the center point and the points on the surface. Finally, we express them using multiple colors and draw the colors representing the distances at the initial position on the hypersphere. Then, we observe the temporal changes of these colors generated by the temporal evolution of the distances. Application of the proposed method to chaotic dynamics results in the appearance of stripe patterns on the surface of the hypersphere over time. The results indicate that we can detect the stretch-and-fold mechanism, or the horse-shoe structure embedded in chaotic dynamics. We also discussed the reason for the generation of the stripe pattern under the framework of the proposed method.
- 出版日期2012-11
