几种混沌控制和同步方法及其在生物医学模型中的应用研究

发布时间：2018-11-14 21:03

【摘要】：由于自然界的非线性本质,混沌科学的发展受到了越来越多的重视。二十多年前,混沌控制和同步思想的提出获得了众多学者的广泛关注,并取得了许多应用成果。生物医学领域中,包括心脏和血管系统、大脑神经网络系统和流行性疾病中都已有混沌和混沌同步现象发现。因此,寻找新的混沌分析工具,完善混沌控制和同步方法,并探索其在生物和医学领域中的应用是非常有意义的工作。本论文对混沌系统的脉冲控制和同步方法、线性广义同步方法、反同步方法和自适应控制方法进行了研究；使用这些方法对肌型血管模型、延迟神经网络和季节性流行病模型中的混沌进行了控制和同步分析；并给出了其生物和医学背景下的意义。论文共含五章,第一章概述了本文所研究问题的背景和国内外研究情况,并给出了本文的主要内容。论文的主要研究工作在第二到第五章,具体内容如下： (1)提出了一种新的脉冲控制和同步方法,不同于以往的一些脉冲控制和同步方法,该方法的优点在于脉冲控制增益矩阵和脉冲间隔都是可变的。同时还可计算出脉冲控制和同步可以实现的脉冲间隔的估计上限值。通过4维统一超混沌系统和3维混沌系统验证了该方法的有效性。应用该脉冲方法研究了含周期性刺激的肌型血管数学模型的同步,从理论上证明了可以通过脉冲同步控制,使疾病状态下血管的运动状态与正常血管达到同步,以实现对疾病的治疗。结合临床意义,分析了可变脉冲控制矩阵和脉冲间隔的重要应用价值。 (2)提出了一种新的广义同步方法来实现不同混沌系统间的线性广义同步,该方法统一了多种已经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、旋转同步等。能够在驱动系统参数未知的前提下,通过设计合适的控制器和参数更新法则,准确识别出未知参数。 (3)基于微分方程组不变原理,提出了状态和非状态反馈反同步方法,并应用于一类延迟混沌神经网络中。该方法使用的自适应反馈力比一些已知的方法中所需使用的反馈力要小,且不需要提前知道连接矩阵；在参数不匹配和噪声干扰下也能够较好的实现系统的反同步。 (4)研究了季节性流行病模型中混沌现象的控制,验证了对季节性流行病中单一群体的控制不能将疾病流行态势控制到无病状态；且某些情况下通过增加受控群体的种类并不能使控制效果变得更加优化。
[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.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：R-332;O231 ;O415.5

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