本文選題：復(fù)雜網(wǎng)絡(luò)　切入點：分數(shù)階微分系統(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】：隨著信息技術(shù)的發(fā)展,復(fù)雜網(wǎng)絡(luò)已被廣泛應(yīng)用于描述各種人工和自然系統(tǒng),如社交網(wǎng)絡(luò),互聯(lián)網(wǎng),神經(jīng)網(wǎng)絡(luò),生物網(wǎng)絡(luò)。復(fù)雜網(wǎng)絡(luò)是21世紀重點研究課題之一,吸引了大量不同領(lǐng)域的研究人員,建立了一些經(jīng)典的網(wǎng)絡(luò)模型來描述現(xiàn)實生活中各類真實的復(fù)雜系統(tǒng)。深入研究復(fù)雜網(wǎng)絡(luò)對更好地理解各類真實復(fù)雜系統(tǒng)具有非常重大的現(xiàn)實意義。同步作為復(fù)雜網(wǎng)絡(luò)主要的動力學(xué)行為,一直備受研究者的青睞。復(fù)雜網(wǎng)絡(luò)同步的早期研究只針對整數(shù)階微分系統(tǒng)節(jié)點,而分數(shù)階微分系統(tǒng)能夠更好的描述現(xiàn)實網(wǎng)絡(luò)中具有的記憶屬性,因而對于分數(shù)階復(fù)雜網(wǎng)絡(luò)同步控制研究已經(jīng)成為了新的研究課題。本文基于Lyapunov穩(wěn)定性理論、非線性分數(shù)階穩(wěn)定性理論和LaSalle不變性原理分析了兩個耦合分數(shù)階復(fù)雜網(wǎng)絡(luò)的混合同步問題。通過引入分數(shù)階控制器,使得具有分數(shù)階混沌或超混沌節(jié)點的兩個耦合復(fù)雜網(wǎng)絡(luò)達到混合同步狀態(tài)。并提出了實現(xiàn)包括驅(qū)動-響應(yīng)網(wǎng)絡(luò)外同步和每一個網(wǎng)絡(luò)內(nèi)同步的充分條件。結(jié)合理論分析和仿真實驗驗證出,在系統(tǒng)參數(shù)滿足特定的條件下,兩個耦合網(wǎng)絡(luò)可以達到混合同步狀態(tài)。此外,本文關(guān)注由分數(shù)階混沌系統(tǒng)為節(jié)點構(gòu)成的兩個耦合分數(shù)階復(fù)雜網(wǎng)絡(luò)的投影同步問題,利用非線性分數(shù)階穩(wěn)定性理論和自適應(yīng)控制策略,在響應(yīng)網(wǎng)絡(luò)中添加分數(shù)階控制器,實現(xiàn)了驅(qū)動-響應(yīng)網(wǎng)絡(luò)的投影同步。全文的主要內(nèi)容和創(chuàng)新點如下:(1)利用分數(shù)階微積分定義,深入研究分數(shù)階微分系統(tǒng)所構(gòu)成的復(fù)雜網(wǎng)絡(luò)。在分數(shù)階復(fù)雜網(wǎng)絡(luò)同步研究中,考慮到階數(shù)對系統(tǒng)控制作用的影響,選用控制參數(shù)為分數(shù)階微分形式的控制器,并通過實驗驗證了此控制器的有效性。(2)針對驅(qū)動-響應(yīng)分數(shù)階復(fù)雜網(wǎng)絡(luò)的混合同步進行了詳細闡述。復(fù)雜網(wǎng)絡(luò)中包含大量相互作用的節(jié)點,網(wǎng)絡(luò)的拓撲結(jié)構(gòu)直接影響單個復(fù)雜網(wǎng)絡(luò)的內(nèi)同步,兩個不同復(fù)雜網(wǎng)絡(luò)之間的外同步更多地依賴于系統(tǒng)中的控制器。本文利用分數(shù)階非線性穩(wěn)定性理論、Lyapunov穩(wěn)定性理論及LaSalle不變性原理,給出了兩個耦合分數(shù)階復(fù)雜網(wǎng)絡(luò)混合同步的充分條件。最后,通過分數(shù)階超混沌Lorenz、混沌Lorenz和超混沌Chen系統(tǒng)的數(shù)值仿真驗證了理論結(jié)果的正確性。(3)分析了兩個耦合分數(shù)階復(fù)雜網(wǎng)絡(luò)的投影同步問題。根據(jù)投影同步定義,利用分數(shù)階非線性穩(wěn)定性理論和自適應(yīng)控制技術(shù),設(shè)計出分數(shù)階控制器,在該控制器的作用下實現(xiàn)了驅(qū)動-響應(yīng)網(wǎng)絡(luò)的投影同步。最后,通過分數(shù)階混沌Lorenz、分數(shù)階混沌Liu和分數(shù)階混沌Chen系統(tǒng)的數(shù)值仿真對投影同步控制效果進行了驗證。
[Abstract]:With the development of information technology, complex networks have been widely used to describe various artificial and natural systems, such as social networks, the Internet, neural networks, biological networks. Attracted a lot of researchers from different fields, Some classical network models are established to describe various real complex systems in real life. It is very important to study complex networks for better understanding of real complex systems. Synchronization is a complex system. The main dynamic behavior of the network, The early research on synchronization of complex networks is focused on the nodes of integer-order differential systems, and fractional differential systems can better describe the memory properties of real networks. Therefore, the research of fractional complex network synchronization control has become a new research topic. This paper based on Lyapunov stability theory, Nonlinear fractional stability theory and LaSalle invariance principle are used to analyze the mixed synchronization problem of two coupled fractional order complex networks. Two coupled complex networks with fractional chaotic or hyperchaotic nodes reach the state of mixed synchronization. Sufficient conditions for the realization of external synchronization including drive-response network and synchronization within each network are proposed. The theory is combined with the theory. The analysis and simulation results show that, Under the condition that the system parameters satisfy certain conditions, two coupled networks can achieve mixed synchronization state. In addition, this paper focuses on the projective synchronization problem of two coupled fractional order complex networks composed of fractional chaotic systems as nodes. Using nonlinear fractional stability theory and adaptive control strategy, a fractional order controller is added to the response network. The projective synchronization of drive-response network is realized. The main contents and innovations of this paper are as follows: 1) by using the fractional calculus definition, the complex network formed by fractional differential system is deeply studied. In the research of fractional order complex network synchronization, Considering the influence of order number on the control of the system, the control parameter is chosen as the controller in fractional differential form. The effectiveness of the controller is verified by experiments. (2) the hybrid synchronization of drive-response fractional complex networks is described in detail. The complex networks contain a large number of interacting nodes. The topology of the network directly affects the internal synchronization of a single complex network. The external synchronization between two different complex networks is more dependent on the controller in the system. In this paper, the fractional order nonlinear stability theory and the LaSalle invariance principle are used. Sufficient conditions for hybrid synchronization of two coupled fractional-order complex networks are given. Finally, Numerical simulation of fractional hyperchaos, chaotic Lorenz and hyperchaotic Chen system verifies the correctness of the theoretical results. The projection synchronization problem of two coupled fractional order complex networks is analyzed, according to the definition of projection synchronization. Based on fractional nonlinear stability theory and adaptive control technology, a fractional order controller is designed. The projective synchronization of driving-response network is realized under the action of the controller. Finally, The effect of projection synchronization control is verified by numerical simulation of fractional chaotic Lorenz, fractional chaotic Liu and fractional chaotic Chen system.
【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】：O157.5;O231

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