Chaotic behavior of logistic map in superior orbit and an improved chaos-based traffic control model

Abstract

With a vital role of discrete chaos, standard logistic map has found a celebrated place in the dynamics of chaos theory and in various applications of science, such as a discrete traffic flow model, image encryption in cryptography, secure communication, and weather forecasting. Traditionally, this discrete chaos is controlled by one parameter $$\lambda $$ using Picard orbit, a one-step feedback procedure. This article presents a one-step forward, applying Mann orbit (superior orbit) the chaotic properties such as period-doubling, period-3 window, and Lyapunov exponent of the standard logistic map is investigated. The results are illustrated analytically and experimentally followed by concluding remarks and a few counter examples. Due to the extra degree of freedom in parameter $$\lambda $$ , the map provides improved chaotic properties that increases the performance of dynamical phenomena. Moreover, this study describes an improved chaos-based discrete traffic control model. Surprisingly, added new parameter $$\alpha $$ in Mann orbit works as control variable that increases the stability performance of the traffic model.