动力系统

In this paper, we use some algebraic geometry methods to study the construction of χ-invariant algebras of some linear corresponding moduli space of these systems. Moreover, we completely determine the stable and semistable locus of these systems.

本文，我们以代数几何中的一些方法来研究某些线性动力系统的χ-不变代数的构造，并给出这类系统的相应的参量空间的刻划，进一步，完全决定了这类系统的稳定点、半稳定点的轨迹。

The dynamic stability of this system is discussed by the Hopf bifurcation theory and the condition of the limit cycle occurring is given.

应用Hopf分岔理论讨论了时滞动力系统动态稳定性，给出了系统产生极限环的条件，最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响。

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

Because the time series generated from finite difference equation with chaos may also possess exponential distribution of probability density. Additionally, irregular dynamics has ever been attributed to the presence of stochastic noise in many systems, but actually it may result from chaotic process in deterministic system.

近年来对非线性动力系统的深入研究发现：观察到某一过程具有指数型概率密度事件分布并不足以确定它就是泊松过程，由具有混沌行为的有限差分方程所产生的时间序列也可具有指数型概率密度分布；在许多系统中，过去归因于随机噪声的不规则动力学特性，实际上很有可能是由确定性系统中的混沌过程所致。

In mathematical viewpoint, this kind of systems are called non-smooth dynamical systems, i.e., right-hand sides of the systems are not continuous or differentiable.

从数学的观点来看，这一类系统称为非光滑动力系统，即这些系统的右端是不连续或不可微的。

The existence of an attractor is one of the most important characteristics for a dissipative system,the long-time dynamics is completely determined by the attractor of the system.

在这种耗散型的无穷维动力系统中，吸引子的存在性是最重要的特征之一，系统的长时间性态完全被系统的吸引子所决定。

The properties of these models are obtained by studing the decreased dimension models by Liapunov function, matrix theory, monotone dynamics theory, Krasnoselskii technique and so on.

通过研究低维系统，我们就可以得到原系统的性态。在对模型的分析中，运用了构造Liapunov函数法、矩阵理论、单调动力系统理论、Krasnoselskii方法等。

Objective Focusing on minimality of dynamical systems,equivalent descriptions of minimality of some special systems are given.

目的主要对动力系统的极小性进行研究，针对几种特殊的系统给出该系统为极小的等价描述。

Now nonlinear dynamical systems with parametric excitation are one of the most important systems in the theory of nonlinear oscillations.

在非线性振动理论中目前最具代表性的一类系统是含有参数激励的非线性动力系统，在这类系统中有着极其丰富和复杂的动力学行为，如分岔、混沌特性等。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。