平移类混沌系统动力学特性与同步及其应用研究

发布时间：2018-01-20 22:02

本文关键词： 平移类混沌系统动力学特性同宿与异宿轨道 Shil’nikov分岔定理自适应滑模同步　出处：《吉林大学》2017年博士论文　论文类型：学位论文

【摘要】：混沌是非线性动力学系统中较复杂的现象,近年来在医学、生物学、电路及通信等领域都进行了大量深入的研究与应用,取得了丰硕的成果。然而,混沌尚无准确的定义,相关理论体系有待完善,特别是由常微分方程(ODEs)组成的多涡卷混沌系统。针对这些现存问题,本文提出新类型的一阶混沌系统,并从动力学特性、数学证明、同步方法和密码学应用四个方面对其进行详细介绍。论文的写作为完善混沌理论、证明混沌方法、强化混沌同步等方面扩充了理论基础,提供了理论依据。现将本文主要工作内容总结如下:总结了现有混沌理论与混沌同步的研究背景、基本定义与研究方法,为后续章节的写作奠定了理论基础。介绍了几种经典混沌系统,如Lorenz系统、Chen系统以及Lü系统,总结并分析这三类混沌系统的特点。本文提出三个新的能产生N个涡卷吸引子的混沌系统,并把这三个系统分别命名为:平移混沌子系统、平移-2混沌子系统和平移-3混沌子系统,统一称为平移类混沌系统。对平移类混沌系统中三个子系统的动力学特性做了详细分析,如平衡点的位置与数量、耗散性条件、不同参量变化的分岔图、Lyapunov指数、Pioncaré映射等,并给出电路设计原理图。从而,完善了一阶混沌系统的理论体系。为了保证理论结果的严密性,从两个不同角度证明了平移类混沌系统中两个子系统混沌特性,分别是:(1)基于待定系数法,证明平移混沌子系统;(2)基于Si'lnikov分岔的同宿、异宿轨道定理法,证明平移-2混沌子系统。理论分析表明,在两子系统中,同宿轨道和异宿轨道共同决定了各自吸引子的几何结构。分析并选取了已经存在的混沌同步方法,实现了平移类混沌系统中三个子系统的自同步与异同步。数值仿真结果表明,分别设计的参数未知自适应滑模控制器,使系统在原点附近具有很好的同步性效果。从而在通信传输、信号处理、数字加密等领域具有潜在的应用价值。将平移混沌系统应用到图像加密与解密领域。针对lena图像提出基于混沌系统的加密与解密算法,并详细描述了两种不同的攻击方式:明文攻击和密文攻击。对研究的密码系统,首先,图像的行与列采用Logistic映射干扰其像素间的相关性。其次,利用平移混沌子系统混合图像的结构与像素,生成密钥流。仿真结果显示,本文提出的加密部分可以在不对图像密钥做任何了解的情况下完成。解密部分,只需要了解加密时设置的初值就能完全破解加密系统。
[Abstract]:Chaos is a complex nonlinear dynamic phenomena in the system, biology in medicine, in recent years, the circuit and communication field are carried out extensive and in-depth research and application, and achieved fruitful results. However, there is no accurate definition of chaos, the relevant theoretical system needs to be improved, especially by ordinary differential equations (ODEs) multi scroll chaotic system composition. To solve these problems, this paper presents a new type of chaotic system, and the dynamic characteristics of mathematical proof, four aspects of synchronization method and application of cryptography is introduced in detail. The thesis writing as the perfect chaos theory, chaos proof method, strengthen the chaotic synchronization is expanded by theoretical basis. To provide a theoretical basis. The main contents of this paper are summarized as follows: summarized the existing theory of chaos and chaos synchronization of the research background, basic concepts and research methods, for the subsequent chapters. The writing has laid a theoretical foundation. This paper introduces several classical chaotic systems, such as Lorenz system, Chen system and L system, summarize and analyze the characteristics of three kinds of chaotic systems. This paper proposes three new N can produce a scroll chaotic system and the three system are respectively named: translation chaotic system, chaotic system and translation translation of -2 -3 chaotic system, unified chaotic system called the translation. The dynamic characteristics of the three subsystems of translation class of chaotic systems in detail, such as the number and location of the equilibrium point, dissipative condition, bifurcation diagram, different parameters of the Lyapunov index, Pioncar mapping principle, and gives the circuit design. Thus, improve the theoretical system of a chaotic system. In order to ensure the tightness of the theoretical results, from two different angles that translation class of chaotic systems with two subsystems of chaos Features are: (1) based on the method of undetermined coefficients, proved the shift chaotic system; (2) based on the Si'lnikov bifurcation of homoclinic, heteroclinic orbit theorem, prove the translation of -2 chaotic system. Theoretical analysis shows that, in the two systems, homoclinic orbits and heteroclinic orbits jointly determined the geometric structure of their respective attractors the analysis and selection of the chaotic synchronization method already exists, the three subsystems in the system translation class of chaotic self synchronization and different synchronization. Numerical simulation results show that the adaptive sliding mode controller with unknown parameters were designed, the system has a good effect on the synchronization and signal processing. Near the origin in communication, that has the potential application value of digital encryption and other fields. The translation of the chaotic system is applied to image encryption and decryption for Lena images is proposed. Chaotic encryption and decryption algorithm, and a detailed description of the Two different types of attacks: plaintext and ciphertext attack on the password system., first of all, the rows and columns of the image by mapping the pixel correlation between Logistic interference. Secondly, using the translation structure and pixel chaotic system mixed image, generate a key stream. The simulation results show that the proposed encryption part can be do not know in any case. Image key decryption section, only need to set the initial value to understand encryption completely break the encryption system.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP309.7;O415.5

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