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 α. Analytical as well as numerical simulations are demonstrated to examine the period-doubling and Lyapunov exponent properties for some particular values of parameter α. Moreover, it is speculated that the superiority in chaos may be used in chaos-based cryptography, in the future.

中文翻译：

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调制物流系统的离散混沌化

近几十年来，差分方程的离散混沌化因其在密码学、交通控制模型、安全通信、天气预报和工程等众多科学分支中的巨大应用而引起了院士和学者的广泛关注。在本文中，研究了调制逻辑系统，并通过倍周期分岔、周期三轨道和李雅普诺夫指数特性报告了优越的混沌。有趣的是，由于有序参数的额外自由度的存在，调制系统承认了混沌的优越性α. 分析和数值模拟被证明可以检查某些特定参数值的周期倍增和李雅普诺夫指数特性α. 此外，据推测，未来混沌的优越性可能会用于基于混沌的密码学。