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The qualitative analysis of a difference equation of population growth

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Summary

The difference equation f b :[0,1]−[0,1] defined by f b (x)=b x(1−x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (f b )i is given by

$$N_i = 1 + \left( {\frac{{1 + \sqrt 5 }}{2}} \right)^i + \left( {\frac{{1 - \sqrt 5 }}{2}} \right)^i$$

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Authors and Affiliations

  1. Mathematics Department, University of California, Berkeley, Cal., USA

    S. Smale

  2. Mathematics Department, Northwestern University, Evanston, Ill., USA

    R. F. Williams

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  1. S. Smale
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  2. R. F. Williams
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Smale, S., Williams, R.F. The qualitative analysis of a difference equation of population growth. J. Math. Biology 3, 1–4 (1976). https://doi.org/10.1007/BF00307853

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  • DOI: https://doi.org/10.1007/BF00307853

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