Abstract
In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic map $${x_{n + 1}} = {r_n}{x_n}\left( {1 - {x_n}} \right),n = 0,1, \ldots ,$$ where {r n } is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.
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