本文選題：分?jǐn)?shù)階 + 傳遞函數(shù)�。� 參考：《江西理工大學(xué)》2017年碩士論文

【摘要】：非線性系統(tǒng)吸引子個(gè)數(shù)代表著該系統(tǒng)的聯(lián)想記憶能力,由于分?jǐn)?shù)階非線性動(dòng)力學(xué)系統(tǒng)可以實(shí)現(xiàn)對(duì)吸引子個(gè)數(shù)的拓展,因此其記憶能力相對(duì)整數(shù)階系統(tǒng)更好。憶阻器由于具有天然的記憶功能,利用憶阻器同樣能夠增大非線性系統(tǒng)的存儲(chǔ)容量。本文主要是針對(duì)非線性動(dòng)力學(xué)系統(tǒng)進(jìn)行構(gòu)建、仿真及穩(wěn)定性分析,深入地研究傳統(tǒng)三維整數(shù)及分?jǐn)?shù)階廣義洛倫茲系統(tǒng),設(shè)計(jì)了一種新的組合型分?jǐn)?shù)階基本單元電路,將其應(yīng)用于異元異構(gòu)分?jǐn)?shù)階整體電路仿真中。同時(shí)設(shè)計(jì)了憶阻函數(shù)多項(xiàng)式分別為可變整數(shù)指數(shù)冪及可變分?jǐn)?shù)指數(shù)冪的一般憶阻器模型,研究了其在簡(jiǎn)約混沌電路系統(tǒng)中的應(yīng)用。本文重點(diǎn)研究?jī)?nèi)容如下:1.構(gòu)建傳統(tǒng)三維整數(shù)階廣義Lorenz系統(tǒng),通過(guò)對(duì)其進(jìn)行動(dòng)力學(xué)特性分析,理論上證實(shí)系統(tǒng)混沌吸引子的存在性;為整數(shù)階系統(tǒng)構(gòu)造電路原理圖,電路仿真結(jié)果顯示該系統(tǒng)具有物理可實(shí)現(xiàn)性。將整數(shù)階系統(tǒng)替換為相應(yīng)地分?jǐn)?shù)階系統(tǒng),同時(shí)引入基于波特圖的線性近似法計(jì)算出一系列(0,1)之間以0.025遞減的傳遞函數(shù)表達(dá)式,并參考4種已有的分?jǐn)?shù)階單元電路,設(shè)計(jì)了一種新的組合型分?jǐn)?shù)階單元電路,并將其與其他四種單元電路組合應(yīng)用于分?jǐn)?shù)階整體電路原理圖中,實(shí)現(xiàn)了異元異構(gòu)分?jǐn)?shù)階電路的仿真,證實(shí)其電路設(shè)計(jì)的可靠性及多樣性。引入兩個(gè)分?jǐn)?shù)階穩(wěn)定性定理,利用該定理對(duì)所設(shè)計(jì)的系統(tǒng)開展穩(wěn)定性分析。2.設(shè)計(jì)憶阻函數(shù)多項(xiàng)式為連續(xù)可變整數(shù)指數(shù)冪的一般憶阻器模型,將其應(yīng)用于最簡(jiǎn)混沌電路系統(tǒng)并進(jìn)行數(shù)值仿真,此時(shí)系統(tǒng)能夠產(chǎn)生一個(gè)混沌吸引子,表明其具有混沌特性;研究線性參數(shù)對(duì)系統(tǒng)混沌特性的影響,設(shè)計(jì)該一般憶阻器模型的電路原理圖,通過(guò)數(shù)值及電路仿真驗(yàn)證憶阻器的三個(gè)本質(zhì)特征。將一般憶阻器模型的憶阻函數(shù)多項(xiàng)式指數(shù)冪由連續(xù)可變正整數(shù)拓展至分?jǐn)?shù),同樣研究系統(tǒng)能否產(chǎn)生吸引子以及系統(tǒng)狀態(tài)是否受其線性參數(shù)的影響;同時(shí)基于指數(shù)、對(duì)數(shù)運(yùn)算電路設(shè)計(jì)乘方運(yùn)算電路,將其應(yīng)用于分?jǐn)?shù)指數(shù)冪一般憶阻器的電路設(shè)計(jì)中,分?jǐn)?shù)指數(shù)冪的憶阻函數(shù)可能在實(shí)際應(yīng)用中更具價(jià)值。將基于一般憶阻器的簡(jiǎn)約混沌電路系統(tǒng)轉(zhuǎn)變?yōu)榉謹(jǐn)?shù)階系統(tǒng),同時(shí)對(duì)其進(jìn)行不同階次組合的數(shù)值仿真。理論分析和數(shù)值、電路仿真均說(shuō)明了分?jǐn)?shù)階系統(tǒng)及分?jǐn)?shù)指數(shù)冪一般憶阻器的物理可實(shí)現(xiàn)性及電路設(shè)計(jì)的有效性,實(shí)驗(yàn)成果對(duì)傳統(tǒng)非線性動(dòng)力學(xué)系統(tǒng)擁有一定參考價(jià)值及意義。
[Abstract]:The number of attractors represents the associative memory ability of the nonlinear system. Because the fractional nonlinear dynamical system can extend the number of attractors, its memory ability is better than that of the integer order system. Because of its natural memory function, the memory capacity of nonlinear systems can also be increased by using it. In this paper, a new combinatorial fractional order basic unit circuit is designed to construct, simulate and analyze the nonlinear dynamics system, deeply study the traditional three-dimensional integer and fractional generalized Lorentz system. It is applied to the whole circuit simulation of heterogeneous fractional order. At the same time, a general memory model with variable integer exponential power and variable fractional exponential power is designed, and its application in reduced chaotic circuit system is studied. The main contents of this paper are as follows: 1: 1. The existence of chaotic attractor of traditional three-dimensional integer order generalized Lorenz system is theoretically proved by analyzing its dynamic characteristics, and the circuit schematic diagram is constructed for integer order system. The circuit simulation results show that the system has physical realizability. The integer order system is replaced by the corresponding fractional order system, and a series of expressions of transfer function with 0.025 decrement between them are calculated by introducing a linear approximation method based on Porter's graph, and four kinds of fractional order cell circuits are referred to. A new combinatorial fractional order circuit is designed and applied to the whole circuit schematic diagram of fractional order, and the simulation of heterogeneous fractional order circuit is realized. The reliability and diversity of the circuit design are verified. Two fractional order stability theorems are introduced to analyze the stability of the designed system. A general memory model with a polynomial of memory function as a continuous variable integer exponent power is designed. The model is applied to the simplest chaotic circuit system and numerically simulated. In this case, the system can produce a chaotic attractor, which shows that it has chaotic characteristics. The influence of linear parameters on the chaotic characteristics of the system is studied. The circuit schematic diagram of the general model is designed, and the three essential characteristics of the demultiplexer are verified by numerical and circuit simulation. In this paper, the polynomial exponential power of memory function is extended from a continuous variable positive integer to a fraction to study whether the system can produce attractors and whether the state of the system is affected by its linear parameters. The logarithmic operation circuit is designed and applied to the circuit design of the general demertiplexer of the fractional exponential power. The memory function of the fractional exponential power may be more valuable in practical application. The reduced chaotic circuit system based on the general amnesia is transformed into a fractional order system, and the numerical simulation of different order combinations is carried out at the same time. Theoretical analysis, numerical simulation and circuit simulation show the physical realizability of fractional order system and fractional exponential power general resistor, and the effectiveness of circuit design. The experimental results have certain reference value and significance for traditional nonlinear dynamic systems.
【學(xué)位授予單位】：江西理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN60

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 劉崇新;;一個(gè)超混沌系統(tǒng)及其分?jǐn)?shù)階電路仿真實(shí)驗(yàn)[J];物理學(xué)報(bào);2007年12期

2 陳向榮;劉崇新;王發(fā)強(qiáng);李永勛;;分?jǐn)?shù)階Liu混沌系統(tǒng)及其電路實(shí)驗(yàn)的研究與控制[J];物理學(xué)報(bào);2008年03期

3 張若洵;楊世平;;分?jǐn)?shù)階共軛Chen混沌系統(tǒng)中的混沌及其電路實(shí)驗(yàn)仿真[J];物理學(xué)報(bào);2009年05期

4 喬曉華;包伯成;;三維四翼廣義增廣Lü系統(tǒng)[J];物理學(xué)報(bào);2009年12期

5 許U，

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