An Analysis of Digraphs and Period Properties of the Logistic Map on Z(pn)

Abstract

This paper corrects some mistakes about three theorems, two figures and some expressions on “finite field” in a literature, and then it analyzes the digraphs and period properties of the logistic map on residue class rings [Formula: see text] and [Formula: see text]. Some theorems and conjectures are proved or given. To validate these properties, we make some numeral experiments and draw the relative figures and tables. So the theoretical analysis and numeral experiments show that there exists periods in the logistic map on [Formula: see text] and on [Formula: see text] and it can be applied in the pseudo-random generators, cryptography, spread spectrum communications and so on.