【摘要】：憶阻混沌系統(tǒng)是典型的非線性系統(tǒng),由于具有對初始條件和系統(tǒng)參數(shù)極為敏感、具有瞬態(tài)混沌、多隱藏吸引子共存以及狀態(tài)轉(zhuǎn)移等與眾不同的物理現(xiàn)象,因而有著極其復(fù)雜的動力學(xué)行為,并為混沌保密通信和實(shí)際工程應(yīng)用提供了更新的有效路徑。本文的研究內(nèi)容具有一定的創(chuàng)新性和實(shí)用性,主要研究成果如下:(1)提出一個四維憶阻混沌系統(tǒng),實(shí)現(xiàn)了其在圖像加密中的應(yīng)用首先,設(shè)計了一種新型雙曲函數(shù)憶阻模型,并將其引入到改進(jìn)的三維混沌系統(tǒng)中,得到了新型的四維雙曲憶阻混沌電路系統(tǒng),通過改變參數(shù)繪出了系統(tǒng)的Lyapunov指數(shù)譜和分岔圖等,進(jìn)而詳細(xì)分析了系統(tǒng)的混沌演化過程。其次,設(shè)計了系統(tǒng)對應(yīng)的硬件實(shí)驗(yàn)電路,實(shí)驗(yàn)結(jié)果與數(shù)值仿真一致;最后,將該系統(tǒng)的混沌序列應(yīng)用到圖像加密中,分析了加密直方圖、相鄰像素相關(guān)性以及抗攻擊能力與密鑰敏感性,仿真結(jié)果表明了憶阻混沌系統(tǒng)具有良好的圖像加密效果。(2)設(shè)計了一個含兩個雙曲憶阻器的五維混沌振蕩電路系統(tǒng),并分析了其多穩(wěn)態(tài)共存的特性首先,結(jié)合經(jīng)典蔡氏電路,設(shè)計了具有兩個雙曲憶阻器的混沌振蕩電路系統(tǒng),并研究了系統(tǒng)隨參數(shù)以及隨憶阻初始狀態(tài)變化的系統(tǒng)運(yùn)行狀態(tài),證實(shí)了提出的雙憶阻器系統(tǒng)不僅依賴于電路參數(shù)的變化,還極端依賴于系統(tǒng)初始條件的改變。此外,五維雙曲憶阻混沌系統(tǒng)具有豐富的多穩(wěn)態(tài)特性,包括了不同拓?fù)浣Y(jié)構(gòu)的混沌吸引子以及周期運(yùn)動的共存,最多時可達(dá)到12種多隱藏吸引子共存。最后,利用幅值放大法有效地進(jìn)行了系統(tǒng)的多穩(wěn)態(tài)吸引子搜索,同樣獲得了不同的周期運(yùn)動與混沌吸引子的共存,搜索結(jié)果與數(shù)值仿真存在較高的一致性。(3)實(shí)現(xiàn)了初始值不同的五維雙憶阻器混沌系統(tǒng)的完全同步和投影同步首先,基于李雅普諾夫穩(wěn)定性理論,設(shè)計了線性反饋控制器,實(shí)現(xiàn)了不同初始值條件下的五維雙憶阻器混沌系統(tǒng)之間的完全同步,控制方案簡單有效,易于實(shí)現(xiàn)。其次,利用主動同步控制法,設(shè)計了合適的非線性反饋控制器,實(shí)現(xiàn)了在不同初始狀態(tài)下的同結(jié)構(gòu)雙曲憶阻混沌系統(tǒng)的投影同步,誤差系統(tǒng)響應(yīng)快,同步性能指標(biāo)高。
[Abstract]:Memorialized chaotic system is a typical nonlinear system. Due to its sensitivity to initial conditions and system parameters, transient chaos, coexistence of multiple hidden attractors and state transition, it is different from others in physical phenomena, such as transient chaos, multi-hidden attractor coexistence and state transition. Therefore, it has extremely complex dynamic behavior, and provides a new and effective path for chaotic secure communication and practical engineering application. The main research results are as follows: (1) A four-dimensional memory chaotic system is proposed, and its application in image encryption is realized. Firstly, a new hyperbolic function memoir model is designed. By introducing it into the improved three-dimensional chaotic system, a new type of four-dimensional hyperbolic memory-resistant chaotic circuit system is obtained. By changing the parameters, the Lyapunov exponent spectrum and bifurcation diagram of the system are plotted, and the chaotic evolution process of the system is analyzed in detail. Secondly, the hardware experiment circuit of the system is designed, and the experimental results are consistent with the numerical simulation. Finally, the chaotic sequence of the system is applied to image encryption. The encrypted histogram, the correlation of adjacent pixels, the anti-attack ability and the key sensitivity are analyzed. The simulation results show that the memory-resistant chaotic system has a good image encryption effect. (2) A five-dimensional chaotic oscillatory circuit system with two hyperbolic memoirs is designed, and its multi-steady-state coexistence characteristics are analyzed. Based on the classical Cai's circuit, a chaotic oscillatory circuit system with two hyperbolic memoirs is designed, and the operating state of the system with the parameter and the initial state of the memory resistance is studied. It is proved that the proposed double-resistor system depends not only on the variation of the circuit parameters, but also on the change of the initial conditions of the system. In addition, the five-dimensional hyperbolic memory-resistant chaotic system has rich multi-stable properties, including the coexistence of chaotic attractors with different topologies and periodic motion, and the coexistence of 12 kinds of multi-hidden attractors can be achieved at most. Finally, the amplitude magnification method is used to search the multistable attractor effectively, and the coexistence of different periodic motion and chaotic attractor is also obtained. There is a high consistency between the search results and numerical simulation. (3) the complete synchronization and projection synchronization of five-dimensional double-resistor chaotic systems with different initial values are realized. Firstly, based on Lyapunov stability theory, a linear feedback controller is designed. The complete synchronization between five-dimensional double-resistor chaotic systems with different initial values is realized. The control scheme is simple, effective and easy to implement. Secondly, using the active synchronization control method, a suitable nonlinear feedback controller is designed to realize the projective synchronization of the hyperbolic memory-resistance chaotic system with the same structure in different initial states. The error system can respond quickly and the synchronization performance index is high.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O415.5;TN60

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