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Exact complexity of the logistic map

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Abstract

The relation between chaotic behavior and complexity for one-dimensional maps is discussed. The one-dimensional maps are mapped into a binary string via symbolic dynamics in order to evaluate the complexity. We apply the complexity measure of Lempel and Ziv to these binary strings. To characterize the chaotic behavior, we calculate the Liapunov exponent. We show that the exact normalized complexity for the logistic mapf: [0,1]→[0,1],f(x)=4x(1−x) is given by 1.

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Authors and Affiliations

  1. Department of Applied Mathematics and Nonlinear Studies, Rand Afrikaans University, 2006, Auckland Park, South Africa

    W. -H. Steeb & R. Stoop

  2. National University of Singapore, Computational Science Programme, Republic of Singapore

    W. -H. Steeb

Authors
  1. W. -H. Steeb
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  2. R. Stoop
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Steeb, W.H., Stoop, R. Exact complexity of the logistic map. Int J Theor Phys 36, 949–953 (1997). https://doi.org/10.1007/BF02435794

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  • DOI: https://doi.org/10.1007/BF02435794

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