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Correlations and spectra of periodic chaos generated by the logistic parabola

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Abstract

We consider the one-parameter family of mappingsf a (x)=4ax(1−x), a, x ε[0, 1] and define an infinite countable set of parameter values ã for which the solutions show observable chaos. Their properties are investigated by means of correlation functions and spectra, which can be interpreted and approximated by separating periodic and chaotic components in the solutions and introducing two simple assumptions on the statistics of the chaotic component.

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Authors and Affiliations

  1. Fachbereich Physik, Philipps-Universität, Renthof 6, D-3550, Marburg, Germany

    Stefan Thomae & Siegfried Grossmann

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  1. Stefan Thomae
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  2. Siegfried Grossmann
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Thomae, S., Grossmann, S. Correlations and spectra of periodic chaos generated by the logistic parabola. J Stat Phys 26, 485–504 (1981). https://doi.org/10.1007/BF01011430

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  • DOI: https://doi.org/10.1007/BF01011430

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