本文關(guān)鍵詞： 平移類(lèi)混沌系統(tǒng) 動(dòng)力學(xué)特性 同宿與異宿軌道 Shil’nikov分岔定理 自適應(yīng)滑模同步　出處：《吉林大學(xué)》2017年博士論文　論文類(lèi)型：學(xué)位論文

【摘要】：混沌是非線(xiàn)性動(dòng)力學(xué)系統(tǒng)中較復(fù)雜的現(xiàn)象,近年來(lái)在醫(yī)學(xué)、生物學(xué)、電路及通信等領(lǐng)域都進(jìn)行了大量深入的研究與應(yīng)用,取得了豐碩的成果。然而,混沌尚無(wú)準(zhǔn)確的定義,相關(guān)理論體系有待完善,特別是由常微分方程(ODEs)組成的多渦卷混沌系統(tǒng)。針對(duì)這些現(xiàn)存問(wèn)題,本文提出新類(lèi)型的一階混沌系統(tǒng),并從動(dòng)力學(xué)特性、數(shù)學(xué)證明、同步方法和密碼學(xué)應(yīng)用四個(gè)方面對(duì)其進(jìn)行詳細(xì)介紹。論文的寫(xiě)作為完善混沌理論、證明混沌方法、強(qiáng)化混沌同步等方面擴(kuò)充了理論基礎(chǔ),提供了理論依據(jù)�，F(xiàn)將本文主要工作內(nèi)容總結(jié)如下:總結(jié)了現(xiàn)有混沌理論與混沌同步的研究背景、基本定義與研究方法,為后續(xù)章節(jié)的寫(xiě)作奠定了理論基礎(chǔ)。介紹了幾種經(jīng)典混沌系統(tǒng),如Lorenz系統(tǒng)、Chen系統(tǒng)以及Lü系統(tǒng),總結(jié)并分析這三類(lèi)混沌系統(tǒng)的特點(diǎn)。本文提出三個(gè)新的能產(chǎn)生N個(gè)渦卷吸引子的混沌系統(tǒng),并把這三個(gè)系統(tǒng)分別命名為:平移混沌子系統(tǒng)、平移-2混沌子系統(tǒng)和平移-3混沌子系統(tǒng),統(tǒng)一稱(chēng)為平移類(lèi)混沌系統(tǒng)。對(duì)平移類(lèi)混沌系統(tǒng)中三個(gè)子系統(tǒng)的動(dòng)力學(xué)特性做了詳細(xì)分析,如平衡點(diǎn)的位置與數(shù)量、耗散性條件、不同參量變化的分岔圖、Lyapunov指數(shù)、Pioncaré映射等,并給出電路設(shè)計(jì)原理圖。從而,完善了一階混沌系統(tǒng)的理論體系。為了保證理論結(jié)果的嚴(yán)密性,從兩個(gè)不同角度證明了平移類(lèi)混沌系統(tǒng)中兩個(gè)子系統(tǒng)混沌特性,分別是:(1)基于待定系數(shù)法,證明平移混沌子系統(tǒng);(2)基于Si'lnikov分岔的同宿、異宿軌道定理法,證明平移-2混沌子系統(tǒng)。理論分析表明,在兩子系統(tǒng)中,同宿軌道和異宿軌道共同決定了各自吸引子的幾何結(jié)構(gòu)。分析并選取了已經(jīng)存在的混沌同步方法,實(shí)現(xiàn)了平移類(lèi)混沌系統(tǒng)中三個(gè)子系統(tǒng)的自同步與異同步。數(shù)值仿真結(jié)果表明,分別設(shè)計(jì)的參數(shù)未知自適應(yīng)滑�？刂破�,使系統(tǒng)在原點(diǎn)附近具有很好的同步性效果。從而在通信傳輸、信號(hào)處理、數(shù)字加密等領(lǐng)域具有潛在的應(yīng)用價(jià)值。將平移混沌系統(tǒng)應(yīng)用到圖像加密與解密領(lǐng)域。針對(duì)lena圖像提出基于混沌系統(tǒng)的加密與解密算法,并詳細(xì)描述了兩種不同的攻擊方式:明文攻擊和密文攻擊。對(duì)研究的密碼系統(tǒng),首先,圖像的行與列采用Logistic映射干擾其像素間的相關(guān)性。其次,利用平移混沌子系統(tǒng)混合圖像的結(jié)構(gòu)與像素,生成密鑰流。仿真結(jié)果顯示,本文提出的加密部分可以在不對(duì)圖像密鑰做任何了解的情況下完成。解密部分,只需要了解加密時(shí)設(shè)置的初值就能完全破解加密系統(tǒng)。
[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.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP309.7;O415.5

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1 劉越;平移類(lèi)混沌系統(tǒng)動(dòng)力學(xué)特性與同步及其應(yīng)用研究[D];吉林大學(xué);2017年

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本文編號(hào)：1449550