Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2024-04-26 DOI:10.1155/2024/9363431
Lina Ding, Pan Wang
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Abstract

To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.
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立方非线性五维膜混沌系统的动力学分析与降维同步掩蔽研究
为了提高混沌系统的复杂性,实现图像信息的有效传输,本文构建了一个具有立方非线性项的五维记忆混沌系统,该系统有四对对称坐标。首先,利用李亚普诺夫指数图、分岔图和吸引子相图对立方非线性记忆混沌系统进行了分析。实验结果表明,在四对对称坐标下,系统不仅存在依赖参数的对称旋转共存吸引子和瞬态混沌现象,还存在依赖于忆阻器初始值的交替混沌循环的超多态性。然后,提出在线性状态变量中加入常数项,探讨线性状态变量的偏移增量对四对对称坐标系统的影响,同时利用 Simulink 对五维混沌系统进行电路仿真,验证其存在性和可实现性。最后,实现了降维系统的同步和图像的保密传输,利用系统的控制电压替换忆阻器的内部状态变量来实现一维降维过程,并设计了自适应同步控制器来实现降维前后的系统同步。在此基础上,将待传输的图像调制成一维阵列,然后进行分数运算和循环运算,结合线性加解密函数和混沌掩码技术,实现了图像的简单加解密过程。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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