發(fā)布時間：2018-06-15 23:47

  本文選題：Lorenz系統(tǒng) + 憶阻器��； 參考：《西南大學》2017年碩士論文

【摘要】：混沌作為自然科學和社會科學中廣泛存在的一種現(xiàn)象,也作為非線性領(lǐng)域內(nèi)一種特殊情況,引起了國內(nèi)外學者的廣泛關(guān)注。目前為止研究混沌的一種廣泛和有效的手段是通過電路進行研究。同時,由于憶阻器的非線性特性,以憶阻器作為非線性元件設計混沌電路也逐漸得到研究人員的關(guān)注。現(xiàn)階段,憶阻混沌電路的設計主要是基于蔡氏電路,采用不同類型憶阻器模型替換蔡氏電路中的非線性電阻。在對混沌電路進行脈沖控制時,主要的研究方案是固定時刻脈沖控制。對憶阻混沌電路的設計和脈沖控制還可作如下考慮:首先,我們可以嘗試挖掘蔡氏電路之外的憶阻混沌電路結(jié)構(gòu);其次,在脈沖控制方案中,變時刻脈沖控制也值得我們進行研究和探討。本文以憶阻器和Lorenz系統(tǒng)為基礎(chǔ),提出了一種新的憶阻Lorenz電路,并進一步研究了憶阻Lorenz電路的特點以及此電路系統(tǒng)在變時刻脈沖控制下的穩(wěn)定性分析。具體的研究內(nèi)容和創(chuàng)新之處如下:1.基于二次型憶阻器模型,采用簡單的電路器件,搭建了二次型憶阻器的電路模型,并將此電路模型應用到Lorenz系統(tǒng)中,組建了憶阻Lorenz電路,基于電路,分析憶阻Lorenz系統(tǒng)的動力學行為和混沌現(xiàn)象。2.基于Lyapunov穩(wěn)定性理論,采用脈沖控制的原理,設計了一種變時刻脈沖控制器,實現(xiàn)了對憶阻Lorenz混沌系統(tǒng)的控制。在證明此控制方法有效性的過程中,通過B-equivalence條件和比較系統(tǒng)的方法,證明了系統(tǒng)在變時刻脈沖控制下與在固定時刻脈沖控制下具有相同的穩(wěn)定性,以此將變時刻脈沖問題轉(zhuǎn)化成固定時刻脈沖問題。通過證明系統(tǒng)在固定時刻脈沖控制下達到穩(wěn)定狀態(tài),實現(xiàn)了變時刻脈沖控制憶阻Lorenz混沌系統(tǒng),并通過數(shù)值仿真進行了驗證。
[Abstract]:Chaos, as a widespread phenomenon in natural science and social science, is also a special case in nonlinear field, which has attracted the attention of scholars both at home and abroad. So far, one of the most effective ways to study chaos is by circuit. At the same time, because of the nonlinear characteristics of the resistive device, the design of chaotic circuit using the resistor as a nonlinear element has gradually attracted the attention of researchers. At present, the design of amnesia chaotic circuit is mainly based on Chua's circuit. Different types of amnesia models are used to replace the nonlinear resistor in Chua's circuit. In the pulse control of chaotic circuit, the main research scheme is fixed time pulse control. The design and pulse control of amnesia chaotic circuit can also be considered as follows: first, we can try to excavate the structure of amnesia chaotic circuit other than Chua's circuit; secondly, in the pulse control scheme, Variable time pulse control is also worth our research and discussion. In this paper, a new type of amnesia Lorenz circuit is proposed based on the resistive device and Lorenz system. The characteristics of the circuit and the stability analysis of the circuit system under the variable time pulse control are further studied. The specific research contents and innovations are as follows: 1. Based on the model of quadratic type amnesia, the circuit model of quadratic type amnesia is built by using simple circuit device. The circuit model is applied to Lorenz system, and the circuit of amnesia Lorenz is constructed, which is based on circuit. The dynamical behavior and chaotic phenomena of Lorenz system are analyzed. Based on Lyapunov stability theory and the principle of pulse control, a variable time pulse controller is designed to control Lorenz chaotic system. In the process of proving the effectiveness of this control method, it is proved that the system has the same stability under the variable time pulse control and the fixed time pulse control through the B-equivalence condition and the comparison system method. In this way, the variable time pulse problem is transformed into the fixed time pulse problem. It is proved that the system is stable under the control of pulse at fixed time, and the Lorenz chaotic system is controlled by variable time pulse, and verified by numerical simulation.
【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN60

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本文編號：2024198