标准Logistic正弦平方映射的复杂混沌动力学研究

Pub Date : 2021-11-01 DOI:10.2478/auom-2021-0041
S. Kumari, Renu Chugh, Radu Miculescu
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引用次数: 4

摘要

为了改善混沌系统的稳定性,本文建立了一种将Mann轨道上的logistic映射和正弦平方映射(两步反馈过程)相结合的非线性动力系统,并将其命名为标准logistic正弦平方映射(SLSSM)。本文的目的是通过引入不动点和稳定性分析、时间序列表示、分岔图和李亚普诺夫指数等多个方面来研究所提映射(SLSSM)的整体动力学行为。此外,我们表明我们的地图明显优于现有的其他一维地图。研究了通过合理选择控制参数可以控制SLSSM的混沌和复杂行为。此外,收敛和稳定的范围可以大大增加。这种新系统(SLSSM)可用于密码学和混沌同步的研究。
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On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map
Abstract In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.
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