Probability Distributions of the Level Crossing Intervals of the Chaotic Process Generated by the Logistic Map.

The statistical characteristics of the level crossing intervals of the chaotic process generated by the logistic map have been studied. In the previous works, the probability distributions Pn of the crossing intervals for this type of chaotic process have been derived only in the form of recursive expressions. In this paper the probability distributions p0 and p1 are studied by the help of Tent-map, and they are obtained in the form of explicit expressions, instead of recursive expressions. The numerical calculations for these quantities become simple and accurate. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]