A Study on Relationship Between Period and Number of Divisions in Piecewise Logistic Map over Integers

The piecewise logistic map proposed by Wang, Liu and Lei provided a wider range of the control parameter than one by the logistic map. However, it is not clear enough to describe relations between the number of divisions and properties of the map. In this paper, we investigate how the period and link length change with respect to number of divisions. As a result, we confirmed period and link length increases or decreases periodically. Further, we confirmed randomness of long period sequence comparable to the randomness of logistic map over integers with high available bits for 2 bits.