A novel discrete memristive hyperchaotic map with multi-layer differentiation, multi-amplitude modulation, and multi-offset boosting.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0235055
Xinyan Wang, Yuqi Wei, Xu Sun, Zhenyi Fan, Baoxiang Du
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引用次数: 0

Abstract

In recent years, the introduction of memristors in discrete chaotic map has attracted much attention due to its enhancement of the complexity and controllability of chaotic maps, especially in the fields of secure communication and random number generation, which have shown promising applications. In this work, a three-dimensional discrete memristive hyperchaotic map (3D-DMCHM) based on cosine memristor is constructed. First, we analyze the fixed points of the map and their stability, showing that the map can either have a linear fixed point or none at all, and the stability depends on the parameters and initial state of the map. Then, phase diagrams, bifurcation diagrams, Lyapunov exponents, timing diagrams, and attractor basins are used to analyze the complex dynamical behaviors of the 3D-DMCHM, revealing that the 3D-DMCHM enters into a chaotic state through a period-doubling bifurcation path, and some special dynamical phenomena such as multi-layer differentiation, multi-amplitude control, and offset boosting behaviors are also observed. In particular, with the change of memristor initial conditions, there exists an offset that only homogeneous hidden chaotic attractors or a mixed state offset with coexistence of point attractors and chaotic attractors. Finally, we confirmed the high complexity of 3D-DMCHM through complexity tests and successfully implemented it using a digital signal processing circuit, demonstrating its hardware feasibility.

具有多层微分、多振幅调制和多偏移增强功能的新型离散记忆超混沌图。
近年来,在离散混沌图中引入忆阻器因其提高了混沌图的复杂性和可控性而备受关注,特别是在安全通信和随机数生成等领域显示出广阔的应用前景。本文构建了一种基于余弦忆阻器的三维离散忆阻器超混沌图(3D-DMCHM)。首先,我们分析了该图的固定点及其稳定性,结果表明该图既可以有线性固定点,也可以没有固定点,其稳定性取决于图的参数和初始状态。然后,利用相图、分岔图、Lyapunov 指数、时序图和吸引子盆地来分析 3D-DMCHM 的复杂动力学行为,发现 3D-DMCHM 通过周期加倍分岔路径进入混沌状态,并观察到一些特殊的动力学现象,如多层分化、多振幅控制和偏移提升行为。特别是,随着忆阻器初始条件的改变,存在仅有同质隐性混沌吸引子的偏移或点吸引子与混沌吸引子共存的混合状态偏移。最后,我们通过复杂性测试证实了 3D-DMCHM 的高复杂性,并利用数字信号处理电路成功实现了它,证明了其硬件可行性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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