一种用于高安全性通信的三维分数阶混沌系统的动力学分析及其电子电路实现

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Girma Adam Beyene, Fahdil Rahma , Karthikeyan Rajagopal, Abdul-Basset A. Al-Hussein, Salah Boulaaras
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引用次数: 0

摘要

本文设计了一个三维分数阶混沌系统(FOCS);通过引入非线性函数及其参数值,平衡可以呈现各种形状和形式。为了了解系统在不同条件和参数值下的行为,通过解析和数值方法进行了动力学分析。该分析采用了相位肖像、李雅普诺夫指数(LEs)、分岔分析和李雅普诺夫光谱等技术。该系统展示了与具有整数值的常规混沌系统相比更复杂的吸引子,特别是如果我们将分数阶q设置为0.97。这一特性使得它非常适合于开发保密通信系统。此外,还利用一个电子电路开发了一个实际实现,以展示其系统的可行性。使用两级加密技术构建了一个安全的通信系统。通过直方图、相关性和谱图调查等测试验证了所提出的加密算法。原始信号与被加密信号的加密相关系数为0.0010,对盗版攻击具有较强的防御能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation

Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation

This article, a 3D fractional-order chaotic system (FOCS) is designed; system holds Equilibria can take on various shapes and forms by introducing a nonlinear function and the value of its parameters. To comprehend the system’s behavior under diverse conditions and parameter values, a dynamical analysis is conducted through analytical and numerical means. This analysis employs techniques like phase portraits, Lyapunov exponents (LEs), bifurcation analysis, and Lyapunov spectra. The system demonstrates attractors that are more intricate compared to a regular chaotic system with an integer value, specifically if we set the fractional order q to 0.97. This characteristic makes it highly appropriate for developing secure communication systems. Moreover, a practical implementation has been developed using an electronic circuit to showcase its feasibility of the system. A secure communication system was built using two levels of encryption techniques. The propose sound encryption algorithm is verified through tests like histogram, correlation, and spectrogram investigation. The encryption correlation coefficient between the original signal and the encrypted one is 0.0010, this result shows a strong defences against pirate attacks.

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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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