本文關(guān)鍵詞： 憶阻器 分?jǐn)?shù)階系統(tǒng) 穩(wěn)定性分析 混沌現(xiàn)象 水印加密 滑�？刂�　出處：《安徽大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：混沌學(xué)涉及自然科學(xué)與社會科學(xué)等眾多領(lǐng)域,它是當(dāng)今世界科學(xué)研究的前沿,而混沌電路的動力學(xué)以及其應(yīng)用可以說是混沌學(xué)的核心問題。憶阻器作為一種全新的非線性電路元器件,它的非易失性和記憶性在混沌電路、混沌加密等方向有著巨大的應(yīng)用前景。隨著憶阻器的提出,憶阻混沌電路受到了國內(nèi)外廣泛的關(guān)注,借助簡單的憶阻電路的建模分析可以有效地描述混沌電路的基本特性。近年來有研究表明分?jǐn)?shù)階微積分相比于傳統(tǒng)整數(shù)階微積分更能精確地描述一些特定的物理現(xiàn)象,所以本文將分?jǐn)?shù)階理論應(yīng)用在憶阻混沌系統(tǒng)中,實驗結(jié)果證實在分?jǐn)?shù)階憶阻電路中存在混沌現(xiàn)象,并且這一混沌現(xiàn)象能夠被充分利用也能夠被有效的控制。本文以憶阻混沌系統(tǒng)的復(fù)雜動力學(xué)現(xiàn)象為研究背景,從整數(shù)階憶阻系統(tǒng)入手,在整數(shù)階混沌系統(tǒng)的基礎(chǔ)上推導(dǎo)出其分?jǐn)?shù)階形式,并對其動力學(xué)進(jìn)行了深入的研究。同時,將混沌現(xiàn)象運(yùn)用在水印加密算法中,從而有效地提高了算法的保密性。最后為了抑制混沌行為的發(fā)生,提出了分?jǐn)?shù)階滑�？刂破鳌Ｈ闹饕膭�(chuàng)新點如下:(1)以簡單的整數(shù)階憶阻器混沌電路模型為研究起點,建立了分?jǐn)?shù)階憶阻器混沌電路的動力學(xué)模型,并利用李雅普諾夫間接法對其穩(wěn)定性進(jìn)行了分析。同時關(guān)注系統(tǒng)的非線性動力學(xué)現(xiàn)象,通過分岔圖以及李雅普諾夫指數(shù)研究了該模型在不同參數(shù)發(fā)生變化時所存在的混沌現(xiàn)象。(2)以混沌系統(tǒng)對初始值的敏感性及其具備的混沌性為研究背景,提出了采用分?jǐn)?shù)階憶阻混沌系統(tǒng)對數(shù)字圖像進(jìn)行水印加密,并通過離散小波變換對密文水印進(jìn)行嵌入以及提取。為了證明該算法的有效性,對算法的抗攻擊性和對密鑰的敏感性進(jìn)行了詳細(xì)的分析。實驗結(jié)果表明基于分?jǐn)?shù)階憶阻混沌系統(tǒng)的水印加密算法具有較高的安全性,與其他算法相比具有更強(qiáng)的不可見性。(3)以分?jǐn)?shù)階憶阻混沌系統(tǒng)為研究對象,為了達(dá)到抑制混沌現(xiàn)象的目的,設(shè)計了一個分?jǐn)?shù)階滑�？刂破�。在確�；Ｐ袨榘l(fā)生的前提下,根據(jù)Lyapunov穩(wěn)定性定理以及滑模理論,選擇積分型的滑模面,建立了函數(shù)切換控制方法下的滑模控制器,并推導(dǎo)出滑�？刂破鲄�(shù)所要滿足的條件。最后實驗結(jié)果分析了控制器在不同參數(shù)下受控系統(tǒng)的穩(wěn)定性,并給出對應(yīng)的時域波形圖,驗證了理論分析的正確性。
[Abstract]:Chaos, which involves many fields such as natural science and social science, is the frontier of scientific research in the world today. The dynamics and application of chaotic circuits are the core problems of chaos. As a new kind of nonlinear circuit components, the non-volatile and memory properties of amnesia are in chaotic circuits. Chaotic encryption and other directions have great application prospects. With the introduction of amnesizer, the circuit of amnesia has received extensive attention at home and abroad. The basic characteristics of chaotic circuits can be described effectively by modeling and analysis of simple memory circuits. Recent studies have shown that fractional calculus can describe some specific physics more accurately than traditional integral calculus. Phenomenon. In this paper, the fractional order theory is applied to the amnesia chaotic system, and the experimental results confirm the existence of chaos in the fractional order circuit. And this chaotic phenomenon can be fully utilized or effectively controlled. In this paper, the complex dynamic phenomenon of the amnesia chaotic system is studied in the context of integer order amnesia system. Based on the integral order chaotic system, the fractional order form is deduced, and its dynamics is deeply studied. At the same time, the chaos phenomenon is applied to the watermark encryption algorithm. Thus, the secrecy of the algorithm is improved effectively. Finally, in order to suppress the occurrence of chaotic behavior. A fractional sliding mode controller is proposed. The main innovations of this paper are as follows: 1) based on the simple chaotic circuit model of integer order amnesia, the dynamic model of fractional order damper chaotic circuit is established. The stability of the system is analyzed by Lyapunov indirect method, and the nonlinear dynamics of the system is concerned. By using bifurcation diagram and Lyapunov exponent, the chaotic phenomena existing in the model with different parameters are studied.) based on the sensitivity of chaotic systems to initial values and their chaotic properties. A fractional order mnemonic chaotic system is proposed to encrypt the digital image and to embed and extract the ciphertext watermark by discrete wavelet transform to prove the effectiveness of the algorithm. The robustness of the algorithm and the sensitivity to the key are analyzed in detail. The experimental results show that the watermark encryption algorithm based on fractional order amnesia chaotic system has high security. Compared with other algorithms, it has stronger invisibility. 3) taking fractional order amnesia chaotic system as the research object, in order to achieve the purpose of suppressing chaos phenomenon. A fractional sliding mode controller is designed. Based on the Lyapunov stability theorem and sliding mode theory, the integral sliding mode surface is selected. The sliding mode controller under the function switching control method is established, and the conditions of the sliding mode controller parameters are deduced. Finally, the stability of the controlled system under different parameters is analyzed by the experimental results. The corresponding time domain waveform diagram is given to verify the correctness of the theoretical analysis.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN60

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