On the Periodic Logistic Map.

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 xn+1=rnxn(1−xn),n=0,1,…,<graphic></graphic> where {<italic>r</italic><italic>n</italic>} is a positive <italic>p</italic>-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable <italic>p</italic>-periodic orbits. This appears to be the first study of the map with variable parameter <italic>r</italic>. [ABSTRACT FROM AUTHOR]