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Pearson-walk visualization of the one-dimensional chaos

Author

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  • Nagai, Yoshinori
  • Ichimura, Atsushi
  • Tsuchiya, Takashi

Abstract

In order to classify fully developed chaos produced by simple one-dimensional maps the Pearson walk which is a special kind of two-dimensional random walk is introduced to visualize, in principle, all the orbits starting from different initial points in one diagram. Chaos of the tent map, standard baker transformation and the logistic map is clearly distinguished from one another in our Pearson-walk representation, which also provides information on not-fully developed chaos that emerges for smaller parameter values for each map. In the present visualization it is also clearly seen how characteristics of the so-called window is differentiated from those of the purely periodic region in the logistic map.

Suggested Citation

  • Nagai, Yoshinori & Ichimura, Atsushi & Tsuchiya, Takashi, 1985. "Pearson-walk visualization of the one-dimensional chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(1), pages 123-154.
    • Handle: RePEc:eee:phsmap:v:134:y:1985:i:1:p:123-154
    DOI: 10.1016/0378-4371(85)90158-X
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    Cited by:

    1. Ghazali, A. & Lallemand, P. & Diep, H.T., 1986. "Spin-glass transition in Heisenberg spin system with ±J random bonds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(3), pages 628-635.

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