Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation

V. Rybin, D. Butusov, Ivan Babkin, Dmitriy Pesterev, Viacheslav Arlyapov
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引用次数: 2

Abstract

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.
用可变中点法获得的离散洛伦兹系统的一些特性及其在混沌信号调制中的应用
非线性科学领域广泛研究了对连续混沌系统应用数值积分技术所产生的各种离散化效应。除了对各种有限差分方案的精度产生负面影响之外,这些效应还可能在实际应用中产生令人惊讶的丰硕成果,例如伪随机数生成、具有改进的扩散和混淆特性的图像加密、混沌路径规划等。近几十年来,基于混沌的通信系统因其高度隐蔽性和宽带传输能力而备受关注。混沌通信系统设计中的一个关键问题是载波信号的调制。由于混沌信号具有类似噪声的特性,因此几乎无法使用与传统谐波信号相同的方法对其进行调制。因此,开发新的调制技术在混沌通信领域具有重大意义。在本研究中,我们研究了利用可控中点数值积分获得的洛伦兹振荡器离散模型,并为基于混沌的通信系统开发了一种新型调制技术。我们通过分岔、吸引盆地和李亚普诺夫频谱分析程序,发现并分析了所研究的有限差分洛伦兹模型动力学中的多稳态现象。通过使用专门设计的测试平台,我们明确表明所提出的调制方法优于常用的参数调制方法,并且在遮蔽性和抗噪性方面几乎等同于最先进的基于对称性的调制方法。此外,所提出的调制技术更易于使用计算机算术实现,特别是在定点硬件中。所报告的结果可有效地应用于设计先进的基于混沌的通信系统或改善现有通信系统架构的特性。
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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