【摘要】：由于自然界的非線性本質(zhì),混沌科學(xué)的發(fā)展受到了越來越多的重視。二十多年前,混沌控制和同步思想的提出獲得了眾多學(xué)者的廣泛關(guān)注,并取得了許多應(yīng)用成果。生物醫(yī)學(xué)領(lǐng)域中,包括心臟和血管系統(tǒng)、大腦神經(jīng)網(wǎng)絡(luò)系統(tǒng)和流行性疾病中都已有混沌和混沌同步現(xiàn)象發(fā)現(xiàn)。因此,尋找新的混沌分析工具,完善混沌控制和同步方法,并探索其在生物和醫(yī)學(xué)領(lǐng)域中的應(yīng)用是非常有意義的工作。本論文對混沌系統(tǒng)的脈沖控制和同步方法、線性廣義同步方法、反同步方法和自適應(yīng)控制方法進行了研究；使用這些方法對肌型血管模型、延遲神經(jīng)網(wǎng)絡(luò)和季節(jié)性流行病模型中的混沌進行了控制和同步分析；并給出了其生物和醫(yī)學(xué)背景下的意義。論文共含五章,第一章概述了本文所研究問題的背景和國內(nèi)外研究情況,并給出了本文的主要內(nèi)容。論文的主要研究工作在第二到第五章,具體內(nèi)容如下： (1)提出了一種新的脈沖控制和同步方法,不同于以往的一些脈沖控制和同步方法,該方法的優(yōu)點在于脈沖控制增益矩陣和脈沖間隔都是可變的。同時還可計算出脈沖控制和同步可以實現(xiàn)的脈沖間隔的估計上限值。通過4維統(tǒng)一超混沌系統(tǒng)和3維混沌系統(tǒng)驗證了該方法的有效性。應(yīng)用該脈沖方法研究了含周期性刺激的肌型血管數(shù)學(xué)模型的同步,從理論上證明了可以通過脈沖同步控制,使疾病狀態(tài)下血管的運動狀態(tài)與正常血管達到同步,以實現(xiàn)對疾病的治療。結(jié)合臨床意義,分析了可變脈沖控制矩陣和脈沖間隔的重要應(yīng)用價值。 (2)提出了一種新的廣義同步方法來實現(xiàn)不同混沌系統(tǒng)間的線性廣義同步,該方法統(tǒng)一了多種已經(jīng)存在的混沌同步方法,如完全同步、投影同步、修改的投影同步、旋轉(zhuǎn)同步等。能夠在驅(qū)動系統(tǒng)參數(shù)未知的前提下,通過設(shè)計合適的控制器和參數(shù)更新法則,準確識別出未知參數(shù)。 (3)基于微分方程組不變原理,提出了狀態(tài)和非狀態(tài)反饋反同步方法,并應(yīng)用于一類延遲混沌神經(jīng)網(wǎng)絡(luò)中。該方法使用的自適應(yīng)反饋力比一些已知的方法中所需使用的反饋力要小,且不需要提前知道連接矩陣；在參數(shù)不匹配和噪聲干擾下也能夠較好的實現(xiàn)系統(tǒng)的反同步。 (4)研究了季節(jié)性流行病模型中混沌現(xiàn)象的控制,驗證了對季節(jié)性流行病中單一群體的控制不能將疾病流行態(tài)勢控制到無病狀態(tài)；且某些情況下通過增加受控群體的種類并不能使控制效果變得更加優(yōu)化。
[Abstract]:Because of the nonlinear nature of nature, the development of chaotic science has been paid more and more attention. More than 20 years ago, the idea of chaos control and synchronization was widely paid attention by many scholars, and a lot of application results were obtained. Chaos and chaos synchronization have been found in biomedical fields, including heart and vascular system, brain neural network system and epidemic diseases. Therefore, it is very meaningful to find new tools for chaos analysis, perfect chaos control and synchronization methods, and explore their applications in biological and medical fields. In this paper, the pulse control and synchronization method, linear generalized synchronization method, anti-synchronization method and adaptive control method of chaotic system are studied. These methods are used to control and synchronize chaos in muscular vascular models, delayed neural networks and seasonal epidemic models, and their biological and medical implications are given. There are five chapters in this paper. The first chapter summarizes the background of this paper and the domestic and foreign research situation, and gives the main content of this paper. The main work of this paper is from the second to the fifth chapters. The main contents are as follows: (1) A new pulse control and synchronization method is proposed, which is different from some previous pulse control and synchronization methods. The advantage of this method is that both the pulse control gain matrix and the pulse interval are variable. At the same time, we can calculate the upper bound of pulse interval which can be realized by pulse control and synchronization. The effectiveness of the proposed method is verified by 4-dimensional unified hyperchaotic system and 3-dimensional chaotic system. The pulse method was used to study the synchronization of the mathematical model of muscular vessels with periodic stimuli. It was proved theoretically that the movement of blood vessels in disease state could be synchronized with that of normal blood vessels by pulse synchronization control. In order to achieve the treatment of disease. Combined with clinical significance, the important application value of variable pulse control matrix and pulse interval is analyzed. (2) A new generalized synchronization method is proposed to realize linear generalized synchronization between different chaotic systems. This method unifies many existing chaotic synchronization methods, such as complete synchronization, projection synchronization and modified projection synchronization. Rotate synchronously, etc. Under the premise of unknown parameters of the drive system, the unknown parameters can be accurately identified by designing appropriate controller and updating rules of parameters. (3) based on the invariant principle of differential equations, the state and non-state feedback anti-synchronization methods are proposed and applied to a class of delayed chaotic neural networks. The adaptive feedback force used in this method is smaller than that used in some known methods, and the connection matrix does not need to be known in advance, and the de-synchronization of the system can be achieved better under the condition of parameter mismatch and noise interference. (4) the control of chaos in seasonal epidemic model is studied, and it is proved that the control of single population in seasonal epidemic can not control the epidemic situation to disease-free; And in some cases, by increasing the number of controlled groups, the control effect is not optimized.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2012
【分類號】：R-332;O231 ;O415.5

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