A Novel Fixed Point Feedback Approach Studying the Dynamical Behaviors of Standard Logistic Map

Abstract

The standard logistic map is one of the oldest and simplest systems which has found a celebrated place in the dynamical systems and in different vital applications of science like image encryption in cryptography, secure communications and traffic control models. Generally, the dynamical systems are characterized by one or more control parameters that determine the dynamical behaviors of the system. Traditionally, the discrete logistic map allows only one parameter [Formula: see text] to determine its complete behavior. This study takes one step forward, using the superior fixed point iterative technique to study the dynamical properties of the discrete logistic map. The proposed technique provides an extra degree of freedom on control parameters that renders superior dynamical properties and may increase the performance of many applications. Analytical analysis as well as numerical simulations are presented to show the effectiveness, flexibility and efficiency of new method.