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A note on global stability in the periodic logistic map

  • * Corresponding author: Rafael Luís

    * Corresponding author: Rafael Luís 
The first and second authors are partially supported by FCT/Portugal through the projects UID/MAT/04459/2019 and UID/MAT/00006/2019, respectively
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  • In this paper, the dynamics of the celebrated $ p- $periodic one-dimensional logistic map is explored. A result on the global stability of the origin is provided and, under certain conditions on the parameters, the local stability condition of the $ p- $periodic orbit is shown to imply its global stability.

    Mathematics Subject Classification: Primary: 37B55, 39A23; Secondary: 37C25, 37C75, 39A30.


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  • Figure 1.  Regions of stability, in the parameter space $ r_{0}O r_1 $, of the fixed points of $ f_1\circ f_0 $, with $ f_i(x) = r_i x(1-x) $, $ i = 0, 1 $

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