不动点方法

Then, introducing the improved straight-line stabilization method to control the chaotic phenomena in the models, a controller is designed to stabilize the biological population in the oribits where the fixed points lie on, thus eliminating the chaotic phenomena in population to keep the population system in persistent existence.

其次采取改进的直线稳定化方法控制模型所存在的混沌现象，设计并求得了使得生物种群稳定到不动点轨道的控制器，最终消除了种群中存在的混沌现象，从而保持了种群系统的持续生存。

In chapter 3, by Brouwer's fixed point theorem, we prove existence of the equilibrium point for high-order Cohen-Grossberg neural networks with delay, and investigate global stability of the equilibrium point by Lyapunov method.

第三章主要通过Brouwer's不动点定理证明了具延迟的高阶Cohen-Grossberg神经网络平衡点的存在性，并且用Lyapunov方法研究了平衡点的全局稳定性。

This paper firstly introduces the concept of least function dependence set and the minimal fixed point theory, and then analyzes the relation between closure of function dependence set and complete lattice, and puts forward analyzes a concrete solution of least function dependence with use of minimal fixed point theory.

本文尝试采用严密的逻辑方法，利用最小不动点理论去求解最小函数依赖集。1最小函数依赖集(1)函数依赖一个数据依赖是关于关系数据库中关系的属性值之间的相关关系的一个命题，它规定了一个关系数据库的规范所满足的完整性约束条件。

The major contributions of this thesis include:(1) proposing a new kind of optimal feedback control, followed by its application to chaos targeting and stabilization of high period unstable periodic orbits ;(2) stabilization of unstable fixed point in chaotic systems using some kind of nonlinear feedback control, and giving sufficient condition for the existence of the controller as well as the synthesis procedure;(3) analyzing the robustness of optimal control in chaotic Lur'e systems under the help of H〓 control theory;(4) finally and most importantly, introducing a novel method of information storage based on discrete time chaotic systems as the application of chaos control, and systematically studying different schemata for implementation, providing a theoretic basis for the design of such new kind of information storage devices with large capacity.

本文的主要工作包括，提出一种新的最优反馈控制，并将之应用于混沌引导控制及混沌系统高周期不稳定周期轨道的镇定控制；针对不动点镇定控制的一类非线性反馈控制器，文中给出该类反馈控制存在的充分条件及设计步骤；文中还利用非线性H〓鲁棒控制理论对Lur'e混沌系统中的最优线性反馈控制进行鲁棒性分析；最后，也是最重要的，作为混沌控制的应用，文中提出一种基于离散时间混沌系统的信息存储方法，系统地分析、研究了实现这种信息存储的不同方案，为以后进行这种新型大容量存储器设计提供了一定的理论依据。

However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

First, the problem of stabilizing a given periodic orbit in a chaotic system is discussed. Then, a method for the stabilization of an unstable focus point is presented, which does not require the location of the focus point. At last, a method for the synchronization of chaotic systems using neural networks is proposed.

首先给出了使系统稳定在某个给定的周期轨道上的方法；接着讨论了如何使系统稳定在某个事先未知的不动点上；最后，提出了一种基于神经网络的混沌系统的同步化方法。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

In chapter 6, we discussed the wavefront solution of a kind of lattice differential equation which derives from diverse fields. We obtained the wavefront solution by using sup-subsolution iteration when the coupled functions are quasimonotone, and by applying Schauder fixed point theorem, we also obtained the wavefront solution when the coupled functions have a different quasimonotone property.

在第六章中，我们对一类从实际问题中抽象出来的二阶时滞格微分方程的行波解进行了讨论，用单调迭代的方法讨论了耦合函数具有拟单调性时行波解的存在性，用不动点的方法讨论了耦合函数具有指数拟单调性时行波解的存在性。

For technical reasons, the method requires the eigenvalues of the solutions at their fixed point is off the unit circle or lies on the unit circle with the Diophantine condition.

作者以前的工作可通过递推序列给出解析的显式解，但由于技术的原因，在方法上要求其解在不动点处的特征值不在单位圆周上或在单位圆周上但满足Diophantine条件。

The control aim was realized. Based on special sliding-mode control with parameter identification, the unified chaos was led to unstable equilibrium point.

基于特殊的滑模控制方法结合参数辨识对含有未知参数的统一混沌系统实现了不稳定不动点的跟踪控制。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。