【摘要】：多渦卷混沌吸引子與傳統(tǒng)的雙渦卷混沌吸引子相比,具有更多的密鑰參數(shù)及更復雜的動力學特性,因此其更適合混沌保密通信。近二十年來,國內(nèi)外研究者對多渦卷混沌吸引子產(chǎn)生方法進行了大量探索。但得到的構(gòu)造方法大體相同,均是通過構(gòu)造不同的非線性函數(shù)從而達到產(chǎn)生多渦卷混沌吸引子的目的。此類方法存在的主要問題是數(shù)學運算復雜,電路實現(xiàn)困難。因此尋找一種簡便的多渦卷實現(xiàn)方法,打破傳統(tǒng)方法中設計各類復雜非線性函數(shù)的限制,將為多渦卷混沌電路走向?qū)嶋H應用產(chǎn)生便利。將第四種基本電子元件憶阻器應用到混沌電路設計中,是近年來混沌電路發(fā)展的一個新方向。與傳統(tǒng)混沌電路相比,憶阻混沌電路具有更復雜的混沌特性。隨著混沌理論在實際工程中應用越來越廣泛,如何更好的利用憶阻器的非線性,設計各類新型憶阻型混沌電路,具有重要的實際意義。著眼于混沌實際應用中的重點問題出發(fā),本論文的主要工作集中在多渦卷混沌吸引子產(chǎn)生方法研究和憶阻混沌電路設計兩個方面。具體研究內(nèi)容及成果總結(jié)如下:(1)提出了一種基于脈沖控制法的混沌多渦卷實現(xiàn)方法。該法只要在雙渦卷混沌系統(tǒng)中特定位置加入合適的脈沖源,即可實現(xiàn)系統(tǒng)平衡點的平移或擴展,從而實現(xiàn)多渦卷混沌吸引子的產(chǎn)生。將該方法成功應用于蔡氏電路,Jerk系統(tǒng)及模擬Lorenz系統(tǒng)中,產(chǎn)生一系列不同的多渦卷和多翼蝴蝶混沌吸引子。相比傳統(tǒng)方法,新方法無需構(gòu)造系統(tǒng)非線性控制函數(shù),及設計復雜實現(xiàn)電路。因此該方法無論在數(shù)學分析還是在電路實現(xiàn)上,都簡化了多渦卷混沌電路的設計。(2)提出了一種復合混沌吸引子的系統(tǒng)實現(xiàn)方法。首先構(gòu)造一個統(tǒng)一的混沌系統(tǒng),即當系統(tǒng)參數(shù)取不同的值時,該系統(tǒng)可分解成兩個子系統(tǒng),相應得到兩類混沌吸引子。然后用脈沖信號去實現(xiàn)系統(tǒng)參數(shù)的不同取值,即可實現(xiàn)子系統(tǒng)混沌吸引子的復合。利用該法成功實現(xiàn)Lorenz系統(tǒng)族下三類吸引子的兩兩復合,Matlab與電路仿真結(jié)果均驗證了該方法的有效性。設計三類不同的憶阻混沌電路,得到一系列不同的混沌吸引子。(3)對蔡氏電路進行改造,設計了一個含兩種憶阻器的五階混沌電路。采用常規(guī)動力學分析手段研究了系統(tǒng)的動力學特性。利用基本元器件設計了憶阻器模擬器,并對所設計混沌電路進行Pspice仿真。得到的Pspice仿真結(jié)果與理論分析一致。(4)采用LC振蕩器和磁控憶阻器設計了一種新的混沌電路。動力學分析表明改變電路參數(shù),可產(chǎn)生雙渦卷、單渦卷、周期態(tài)等不同相軌道。為了實現(xiàn)電路的混沌控制,設計了一種模擬時滯反饋控制電路,Matlab仿真結(jié)果表明該控制器可實現(xiàn)了所提混沌電路的穩(wěn)定控制。最后設計了相應的電路實驗,從示波器上觀察到了混沌吸引子及混沌控制相圖。(5)選擇電流反饋運算放大器作為有源器件,同時巧妙利用該器件的端口特性將四種基本元件(電阻,電容,電感,憶阻器)進行有機結(jié)合,得到一系列新的憶阻混沌電路。仿真結(jié)果顯示這些電路產(chǎn)生一類不同于蔡氏電路的奇怪吸引子,豐富了憶阻混沌吸引子的內(nèi)容。
[Abstract]:The multi-scroll chaotic attractor has more key parameters and more complex dynamic characteristics than the traditional double-scroll chaotic attractor, so it is more suitable for chaotic secure communication. In the past twenty years, many researchers at home and abroad have explored the generation methods of multi-scroll chaotic attractor. The main problem of this kind of method is the complexity of mathematical calculation and the difficulty of circuit realization. Therefore, a simple method of multi-scroll realization is proposed to break the limitation of traditional methods in designing various kinds of complex nonlinear functions, which will lead to multi-scroll chaos. In recent years, the application of memristor, the fourth basic electronic element, to the design of chaotic circuits is a new direction of the development of chaotic circuits. Compared with traditional chaotic circuits, memristor chaotic circuits have more complex chaotic characteristics. With the application of chaotic theory in practical engineering more and more widely, how about It is of great practical significance to make better use of the nonlinearity of memristors to design all kinds of new memristor chaotic circuits. Focusing on the key problems in the practical application of chaos, the main work of this paper focuses on the generation method of multi-scroll chaotic attractors and the design of memristor chaotic circuits. The results are summarized as follows: (1) A chaotic multi-scroll realization method based on pulse control method is proposed. The method can realize the translation or expansion of the equilibrium point of the system and the generation of multi-scroll chaotic attractors by adding a suitable pulse source at a specific position in the dual-scroll chaotic system. A series of different multi-scroll and multi-wing butterfly chaotic attractors are generated in a unified and analog Lorenz system. Compared with the traditional methods, the new method does not need to construct the nonlinear control function of the system and to design complex implementation circuits. A method of system realization of compound chaotic attractor is proposed. Firstly, a unified chaotic system is constructed, that is, when the system parameters are different, the system can be decomposed into two subsystems, and two kinds of chaotic attractors can be obtained accordingly. Three different kinds of memristor chaotic circuits are designed and a series of different chaotic attractors are obtained. (3) The Chua's circuit is reformed and a five-order memristor is designed. Chaotic circuit. The dynamic characteristics of the system are studied by means of conventional dynamic analysis. A memristor simulator is designed with basic components, and the designed chaotic circuit is simulated by Pspice. The results of Pspice simulation are consistent with the theoretical analysis. (4) A new chaotic circuit is designed by using LC oscillator and magnetron memristor. The mechanical analysis shows that different phase trajectories such as double scroll, single scroll and periodic state can be produced by changing the circuit parameters. In order to control the chaos of the circuit, an analog time-delay feedback control circuit is designed. The simulation results of MATLAB show that the controller can realize the stable control of the proposed chaotic circuit. The chaotic attractor and the chaotic control phase diagram are observed in the waveguide. (5) A current feedback operational amplifier is selected as the active device, and four basic elements (resistance, capacitance, inductance, memristor) are combined together to obtain a series of new memristor chaotic circuits by ingeniously utilizing the port characteristics of the device. A strange attractor, which is different from Chua's circuit, is generated, which enriches the content of memristor chaotic attractors.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TM132

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相關(guān)期刊論文 前2條

1 ;Dynamics analysis of chaotic circuit with two memristors[J];Science China(Technological Sciences);2011年08期

2 包伯成;許建平;周國華;馬正華;鄒凌;;Chaotic memristive circuit:equivalent circuit realization and dynamical analysis[J];Chinese Physics B;2011年12期

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本文編號：2220634