# American Institute of Mathematical Sciences

November  2020, 25(11): 4211-4220. doi: 10.3934/dcdsb.2020094

## A note on global stability in the periodic logistic map

 1 Center for Mathematical Analysis, Geometry and Dynamical Systems, University of Lisbon, Portugal, University of Madeira, Funchal, Portugal 2 University of Madeira, Funchal, Portugal, Center of Statistics and Applications, University of Lisbon, Portugal

* Corresponding author: Rafael Luís

Received  July 2019 Revised  October 2019 Published  April 2020

Fund Project: The first and second authors are partially supported by FCT/Portugal through the projects UID/MAT/04459/2019 and UID/MAT/00006/2019, respectively

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.

Citation: Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094
##### References:

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##### References:
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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