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)階非線性動力學(xué)系統(tǒng)可以實現(xiàn)對吸引子個數(shù)的拓展,因此其記憶能力相對整數(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)的存儲容量。本文主要是針對非線性動力學(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。同時設(shè)計了憶阻函數(shù)多項式分別為可變整數(shù)指數(shù)冪及可變分?jǐn)?shù)指數(shù)冪的一般憶阻器模型,研究了其在簡約混沌電路系統(tǒng)中的應(yīng)用。本文重點研究內(nèi)容如下:1.構(gòu)建傳統(tǒng)三維整數(shù)階廣義Lorenz系統(tǒng),通過對其進(jìn)行動力學(xué)特性分析,理論上證實系統(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),同時引入基于波特圖的線性近似法計算出一系列(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,實現(xiàn)了異元異構(gòu)分?jǐn)?shù)階電路的仿真,證實其電路設(shè)計的可靠性及多樣性。引入兩個分?jǐn)?shù)階穩(wěn)定性定理,利用該定理對所設(shè)計的系統(tǒng)開展穩(wěn)定性分析。2.設(shè)計憶阻函數(shù)多項式為連續(xù)可變整數(shù)指數(shù)冪的一般憶阻器模型,將其應(yīng)用于最簡混沌電路系統(tǒng)并進(jìn)行數(shù)值仿真,此時系統(tǒng)能夠產(chǎn)生一個混沌吸引子,表明其具有混沌特性;研究線性參數(shù)對系統(tǒng)混沌特性的影響,設(shè)計該一般憶阻器模型的電路原理圖,通過數(shù)值及電路仿真驗證憶阻器的三個本質(zhì)特征。將一般憶阻器模型的憶阻函數(shù)多項式指數(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;同時基于指數(shù)、對數(shù)運算電路設(shè)計乘方運算電路,將其應(yīng)用于分?jǐn)?shù)指數(shù)冪一般憶阻器的電路設(shè)計中,分?jǐn)?shù)指數(shù)冪的憶阻函數(shù)可能在實際應(yīng)用中更具價值。將基于一般憶阻器的簡約混沌電路系統(tǒng)轉(zhuǎn)變?yōu)榉謹(jǐn)?shù)階系統(tǒng),同時對其進(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現(xiàn)性及電路設(shè)計的有效性,實驗成果對傳統(tǒng)非線性動力學(xué)系統(tǒng)擁有一定參考價值及意義。
[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)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN60

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