本文選題：憶阻器　切入點(diǎn)：憶阻電路系統(tǒng)　出處：《安徽大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：憶阻器,也稱記憶電阻器,是一種具有記憶功能特性的非線性元件,具有區(qū)別于其他三種電路基本元件(電阻器、電容器、電感器)無可比擬的特性,可以記憶經(jīng)過它的電荷數(shù)量,也可以通過控制電流的動態(tài)變化改變其相應(yīng)阻值,并且這種電流的變化特性在斷電時可以繼續(xù)保持,這就使得憶阻器在計(jì)算機(jī)工程、神經(jīng)網(wǎng)絡(luò)、電子工程、通信工程等領(lǐng)域有著非常廣泛的應(yīng)用。在非線性動力學(xué)領(lǐng)域,因?yàn)槠渥鳛樾滦头蔷�性元件構(gòu)成的電路表現(xiàn)出復(fù)雜的動力學(xué)現(xiàn)象,將傳統(tǒng)混沌系統(tǒng)中的非線性元件用憶阻器代替可以構(gòu)成一大類基于憶阻器的混沌電路系統(tǒng)。隨著分?jǐn)?shù)階微積分的發(fā)展,同時考慮搭建電路存在延遲因子,因此將分?jǐn)?shù)階微積分理論引入到憶阻時滯系統(tǒng)模型中,然后對其分析這些系統(tǒng)復(fù)雜的動力學(xué)行為,特別是時滯和分?jǐn)?shù)階等參數(shù)對憶阻混沌系統(tǒng)的動力學(xué)行為影響,是一個值得研究的課題。并且,研究本課題對后期用來搭建混沌電路應(yīng)用于信息安全、保密通信等領(lǐng)域,不僅具有重要的理論研究意義,還具有很好的實(shí)際應(yīng)用前景。本文主要是基于憶阻器的發(fā)展應(yīng)用,分?jǐn)?shù)階和時滯相關(guān)理論的發(fā)展應(yīng)用,將這些理論結(jié)合并應(yīng)用到憶阻器中來搭建混沌電路,提出了多種分?jǐn)?shù)階時滯憶阻模型系統(tǒng);同時,應(yīng)用穩(wěn)定性理論分析系統(tǒng)的參數(shù)(時滯、分?jǐn)?shù)階和系統(tǒng)參數(shù)等)的穩(wěn)定性區(qū)間,得到滿足的多參數(shù)的Hopf分岔理論的橫截條件;最后,具體分析多參數(shù)(時滯、分?jǐn)?shù)階和系統(tǒng)參數(shù)等)下的憶阻混沌系統(tǒng)的動力學(xué)行為。本文的創(chuàng)新點(diǎn)如下:(1)將常規(guī)時滯憶阻電路系統(tǒng)模型推廣到分?jǐn)?shù)階系統(tǒng),建立分?jǐn)?shù)階時滯憶阻電路混沌系統(tǒng)模型,使憶阻混沌系統(tǒng)能更加簡潔規(guī)范的表現(xiàn)出來,揭示憶阻器混沌系統(tǒng)的本質(zhì)特性。(2)利用李亞普羅夫穩(wěn)定性定理,研究這些憶阻混沌系統(tǒng)基于時滯參數(shù)的平衡點(diǎn)穩(wěn)定性的充分條件,得到時滯參數(shù)的穩(wěn)定性區(qū)間,總結(jié)時滯和分?jǐn)?shù)階等參數(shù)對于系統(tǒng)穩(wěn)定性的影響,同時給出對應(yīng)參數(shù)的滿足Hopf分岔的橫截條件。(3)嘗試分析系統(tǒng)的時滯、分?jǐn)?shù)階和系統(tǒng)參數(shù)等參數(shù)應(yīng)用到憶阻混沌電路系統(tǒng)模型中對其動力學(xué)行為的影響。當(dāng)系統(tǒng)時滯和分?jǐn)?shù)階等發(fā)生變化時,揭示分?jǐn)?shù)階時滯憶阻電路系統(tǒng)發(fā)生分岔、周期、混沌等復(fù)雜動力學(xué)行為的根本原因,并且可以得到在不同參數(shù)情況下產(chǎn)生混沌的最小階數(shù),為后期在保密通信應(yīng)用提供廣泛的應(yīng)用前景。
[Abstract]:A memory resistor, also known as a memory resistor, is a kind of nonlinear element with memory characteristics, which is incomparable to the other three basic components of the circuit (resistors, capacitors, inductors). We can remember the amount of charge passing through it, or we can change the corresponding resistance by controlling the dynamic change of the current, and the characteristic of this current can be maintained when the power is off, which makes the amnesia in computer engineering, neural network. Electronic engineering, communication engineering and other fields have been widely used in the field of nonlinear dynamics, because of the complex dynamic phenomena in the circuits which are composed of new nonlinear components. A large class of chaotic circuit systems based on amnesia can be constructed by replacing the nonlinear elements in traditional chaotic systems with a resistor. With the development of fractional calculus, the delay factor of the circuit is considered at the same time. Therefore, the fractional calculus theory is introduced into the model of amnesia time-delay systems, and then the complex dynamic behaviors of these systems are analyzed, especially the effects of parameters such as delay and fractional order on the dynamical behavior of amnesia chaotic systems. It is worth studying. Moreover, this research is not only of great theoretical significance for the application of chaotic circuits to information security, secure communication and other fields, but also of great theoretical significance. This paper is mainly based on the development and application of memristors, fractional order and time-delay related theories, which are combined with these theories to build chaotic circuits. At the same time, stability theory is applied to analyze the stability interval of the system parameters (time delay, fractional order and system parameters, etc.), and the transversal conditions of the multi-parameter Hopf bifurcation theory are obtained. Finally, the dynamical behavior of the amnesia chaotic system with multiple parameters (time delay, fractional order and system parameters etc.) is analyzed in detail. The innovation of this paper is as follows: 1) the model of the conventional time-delay memory circuit system is extended to the fractional order system. The chaotic system model of fractional delay memory circuit is established, which makes the chaotic system more concise and canonical, and reveals the essential characteristics of the chaotic system. In this paper, the sufficient conditions for the stability of these amnesia chaotic systems based on the equilibrium point of the time-delay parameters are studied, the stability interval of the time-delay parameters is obtained, and the effects of the parameters such as time delay and fractional order on the stability of the system are summarized. At the same time, the transversal condition of corresponding parameters satisfying Hopf bifurcation is given. 3) the time-delay of the system is tried to be analyzed. The effects of parameters such as fractional order and system parameters on the dynamical behavior of the chaotic circuit system with amnesia are applied. When the delay and fractional order of the system change, it is revealed that the bifurcation and period occur in the fractional order delay circuit system. The fundamental cause of complex dynamical behavior such as chaos and the minimum order of chaos under different parameters can be obtained, which provides a broad application prospect for the later application of secure communication.
【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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