Discrete Chaotification of a Modulated Logistic System

Abstract

In the last few decades, the discrete chaotification of difference equations has gained the considerable attention of academicians and scholars due to its tremendous applications in many branches of science, such as cryptography, traffic control models, secure communications, weather forecasting and engineering. In this article, a modulated logistic system is studied and superior chaos is reported through period-doubling bifurcation, period-three orbit and Lyapunov exponent properties. It is interesting to see that the modulated system admits the superiority in chaos due to the presence of an extra degree of freedom of an ordered parameter [Formula: see text]. Analytical as well as numerical simulations are demonstrated to examine the period-doubling and Lyapunov exponent properties for some particular values of parameter [Formula: see text]. Moreover, it is speculated that the superiority in chaos may be used in chaos-based cryptography, in the future.