Complex dynamics and encryption application of a 3D dual-memristor oscillatory hyperchaotic map

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-04-19 DOI:10.1016/j.matcom.2025.04.005

Qiang Lai , Chongkun Zhu , Minghong Qin , Zhiqiang Wan

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引用次数: 0

Abstract

Unlike high-dimensional hyperchaotic maps constructed using continuous memristors (CMs), discrete memristors (DMs) are widely favored by researchers because of their unique advantages. In view of this, a novel memristive hyperchaotic map by applying a sinusoidal transformation to one DM and paralleling it with another, while introducing the simple oscillatory term has been proposed. This map exhibits significant structural characteristics, particularly without fixed points. Numerical simulations reveal the dynamical behaviors that dependent on control parameters and the presence of infinite hidden coexisting attractors related to initial values. Furthermore, the map has been successfully applied in the design of a pseudorandom number generator (PRNG). A microcontroller-based digital hardware platform has also been developed to implement this map. Lastly, the application of the map in image encryption provides valuable insights into the use of discrete memristive maps in chaos engineering.

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三维双忆阻振荡超混沌映射的复杂动力学及加密应用

与使用连续忆阻器（CMs）构建的高维超混沌映射不同，离散忆阻器（dm）因其独特的优势而受到研究人员的广泛青睐。鉴于此，本文提出了一种新的记忆超混沌映射，通过对一个DM进行正弦变换并与另一个DM并行，同时引入简单的振荡项。这张地图显示了显著的结构特征，特别是没有固定点。数值模拟揭示了系统的动力学行为依赖于控制参数和存在与初始值相关的无限隐吸引子。此外，该映射还成功地应用于伪随机数发生器（PRNG）的设计。本文还开发了一个基于微控制器的数字硬件平台来实现该地图。最后，映射在图像加密中的应用为离散记忆映射在混沌工程中的应用提供了有价值的见解。

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

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.