本文選題：耦合系統(tǒng)　切入點(diǎn)：白噪聲　出處：《哈爾濱工業(yè)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：近年來(lái),耦合系統(tǒng)的穩(wěn)定性吸引了許多學(xué)者的關(guān)注,很多確定性耦合系統(tǒng)穩(wěn)定性的重要結(jié)果已經(jīng)出現(xiàn)。然而,實(shí)際的耦合系統(tǒng)總是受到各種環(huán)境噪聲的干擾,而環(huán)境噪聲會(huì)使系統(tǒng)的穩(wěn)定性發(fā)生改變。從控制理論的觀點(diǎn)看,研究隨機(jī)耦合系統(tǒng)的穩(wěn)定性非常重要。本文致力于建立幾類隨機(jī)耦合系統(tǒng)的數(shù)學(xué)模型,使用隨機(jī)分析方法分析其穩(wěn)定性,揭示環(huán)境噪聲和耦合結(jié)構(gòu)對(duì)其穩(wěn)定性的影響。論文的主要研究?jī)?nèi)容包括:1.通過(guò)把多擴(kuò)散和白噪聲引入到多斑塊模型中,建立具有多擴(kuò)散的隨機(jī)多斑塊模型。結(jié)合圖論和Lyapunov方法,得到模型指數(shù)穩(wěn)定的Lyapunov型準(zhǔn)則和系數(shù)型判據(jù),并應(yīng)用系數(shù)型判據(jù)分析隨機(jī)耦合振子的均方指數(shù)穩(wěn)定性。研究結(jié)果表明:在有向圖的拓?fù)浣Y(jié)構(gòu)滿足一定條件和白噪聲強(qiáng)度在一定范圍時(shí),隨機(jī)模型是穩(wěn)定的。2.建立具有多擴(kuò)散的比例時(shí)滯隨機(jī)多斑塊模型,分析模型的指數(shù)穩(wěn)定性,得到Lyapunov型準(zhǔn)則和系數(shù)型判據(jù),并應(yīng)用系數(shù)型判據(jù)研究比例時(shí)滯隨機(jī)耦合振子的均方指數(shù)穩(wěn)定性。研究結(jié)果表明:模型的指數(shù)穩(wěn)定性與白噪聲的強(qiáng)度,比例時(shí)滯的系數(shù)和有向圖的拓?fù)浣Y(jié)構(gòu)都有緊密聯(lián)系。3.結(jié)合圖論和Lyapunov方法,研究具有多擴(kuò)散的隨機(jī)多斑塊模型的輸入狀態(tài)穩(wěn)定性,得到輸入狀態(tài)穩(wěn)定的充分準(zhǔn)則,并研究具有輸入控制的隨機(jī)耦合振子的輸入狀態(tài)穩(wěn)定性。研究結(jié)果表明:在適當(dāng)?shù)陌自肼晱?qiáng)度下,模型的輸入狀態(tài)穩(wěn)定性不僅和頂點(diǎn)系統(tǒng)的輸入狀態(tài)穩(wěn)定性有關(guān),而且和有向圖的拓?fù)浣Y(jié)構(gòu)有關(guān)。4.結(jié)合Razumikhin方法和圖論,研究網(wǎng)絡(luò)上耦合中立型隨機(jī)時(shí)滯系統(tǒng)的穩(wěn)定性,得到矩指數(shù)穩(wěn)定的Razumikhin型準(zhǔn)則和系數(shù)型判據(jù),以及幾乎確定指數(shù)穩(wěn)定準(zhǔn)則,并給出數(shù)值算例驗(yàn)證理論結(jié)果的有效性。研究結(jié)果表明:系統(tǒng)的指數(shù)穩(wěn)定性依賴于白噪聲的強(qiáng)度和有向圖的強(qiáng)連通性。5.應(yīng)用Lyapunov方法和M矩陣?yán)碚?分析具有無(wú)窮時(shí)滯和Markov轉(zhuǎn)換的隨機(jī)神經(jīng)網(wǎng)絡(luò)的隨機(jī)穩(wěn)定性、隨機(jī)漸近穩(wěn)定性和全局隨機(jī)漸近穩(wěn)定性,得到保證模型三種隨機(jī)穩(wěn)定的充分條件。研究結(jié)果表明:當(dāng)白噪聲的強(qiáng)度在一定范圍時(shí),模型的三種隨機(jī)穩(wěn)定性與Markov鏈的生成矩陣密切相關(guān)。
[Abstract]:In recent years, the stability of coupled systems has attracted the attention of many scholars, and many important results of the stability of deterministic coupled systems have emerged. However, the actual coupled systems are always disturbed by various kinds of environmental noise. From the point of view of control theory, it is very important to study the stability of stochastic coupled systems. Stochastic analysis is used to analyze its stability and to reveal the influence of environmental noise and coupling structure on its stability. The main contents of this paper include: 1. By introducing multi-diffusion and white noise into the multi-patch model, the main contents of this paper are as follows: 1. A stochastic multi-patch model with multiple diffusion is established. Combining graph theory with Lyapunov method, the exponential stability criteria of Lyapunov type and coefficient type criterion are obtained. The mean square exponential stability of random coupled oscillators is analyzed by using the coefficient type criterion. The results show that when the topological structure of digraphs satisfies certain conditions and the intensity of white noise is in a certain range, The stochastic model is stable .2. the proportional delay stochastic multi-patch model with multiple diffusion is established. The exponential stability of the model is analyzed, and the Lyapunov type criterion and the coefficient type criterion are obtained. The mean square exponential stability of the proportional delay stochastic coupled oscillator is studied by using the coefficient type criterion. The results show that the exponential stability of the model and the intensity of white noise are obtained. The coefficients of proportional delay are closely related to the topological structure of directed graphs. Combining graph theory and Lyapunov method, the input state stability of stochastic multi-patch model with multiple diffusion is studied, and the sufficient criterion of input state stability is obtained. The input state stability of the stochastic coupled oscillator with input control is studied. The results show that the input state stability of the model is not only related to the input state stability of the vertex system, but also to the input state stability of the vertex system under the appropriate white noise intensity. Combined with the Razumikhin method and graph theory, the stability of coupled neutral stochastic time-delay systems on the network is studied. The Razumikhin type criterion and the coefficient type criterion for moment exponential stability are obtained, and the exponential stability criteria are almost certain. Numerical examples are given to verify the validity of the theoretical results. The results show that the exponential stability of the system depends on the intensity of white noise and the strong connectivity of directed graphs .5.Using Lyapunov method and M-matrix theory, The stochastic stability, stochastic asymptotic stability and global stochastic asymptotic stability of stochastic neural networks with infinite delay and Markov transformation are analyzed. Sufficient conditions for ensuring three stochastic stability of the model are obtained. The results show that when the intensity of white noise is in a certain range, the three stochastic stability of the model is closely related to the generation matrix of the Markov chain.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O175

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