Invariant patterns in a non-invertible chaotic map by the directional coloring

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概要

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• We propose a visualization method called the directional coloring for chaotic attractors in planer discrete systems. A color in the hue circle is assigned to the argument determined by the current point and its <I>n</I>-th mapped point. Some unstable <I>n</I>-periodic points embedded in the chaotic attractor become visible as radiation points and they can be accurately detected by combination of this coloring and the Newton's method. For a chaotic attractor in a non-invertible map, we find out invariant patterns around the fixed point and detect its nearest unstable <I>n</I>-periodic point. The computed results of their locations show a fractal property of the system.

著者

• Ueta Tetsushi

  Center for Administration of Information Technology, The University of Tokushima

関連論文

• Invariant patterns in a non-invertible chaotic map by the directional coloring
• Bifurcation analyses of nonlinear dynamical systems: From theory to numerical computations

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